Factor Analysis for Detector Dog C-BARQ for Combined Phase 1 and Phase 2 Data

Version 2.0 of Combined Factor Analysis (No Chasing Data) Using Items with Communality greater than or equal to0.40 from analysis 1.0

lizhare@gmail.com

1 Context

1.1 Overall Factor Analysis Steps

1. Are the data suitable for factor analysis?
   • Bartlett’s Sphericity Test Tests whether correlations are different than zero across all the data. If they are close to zero, there owuld be no common factors to find
   • Kaiser-Meyer-Olkin Criterion Test sampling adequacy, measures the degree to wich each variable predicts all other variables in the data set.
2. Imputation of Missing Variables
   • Generate categorical values for missing data using Multiple Correspondence Analysis/Missing Fuzzy Average Method
3. Calculate between-item Correlations
   • the polychoric (for orderd categorical variables) and regular Pearson correlation are calculated for later use in factor analysis and for checking other aspects of the factor analysis. The polychoric correlation is the input to the actual factor analysis.
4. Estimate Number of Factors
   • Parallel analysis
     
   • Minimim Average Partial (MAP)
5. Run factor analysis for a range of possible number of factors
   • produces
     • measures of model fit
       
     • communalities (how much each item covaries with the other items)
       
     • loadings (correlation between item and factor(s))
6. Evaluate Reliability of Model..
   • alpha
     
   • omega
7. Select best model (number of factors) given model fit statistics and judgement based on understanding of behavior.

1.2 Context Text Description

All data were used in the factorAnalysis1.1.html document you already received.

A series of factoro analyses were run on all items in the file factorAnalysis1.1.html. THe literature suggests doing this so you can compare both statistical measures of how well it fits, and also how logical the grouping of factors is according to knowledge of the subject.

This set of analyses showed that some items had really low communalities, meaning that they didn’t covary much with any of the other items. This means they will not be robust parts of any factor, and they recommend that you remove these from the analysis.

Models with different numbers of factors had different numbers of items with communalities less than 0.4. So a new data set was made for each number of factors, with only the items with communalities of 0.4 or larger.

Because each number of factors require a different data set (different numbers of items), all the steps had to be rerun sstarting with imputation. Those are the models included in this document.

2 Factor Analyses

Testing analyses from 11 - 18 factors.

2.1 11 Factors

2.1.1 Imputation of Missing Items (11 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.1.2 11-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.1.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.4178359^{4} with 2211 DF, p = 0e+00.

2.1.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570731

2.1.3 11-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.1.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 5.8887983^{4} with 2211 DF, p = 0e+00.

2.1.3.2 11-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570731

2.1.4 Between-Item Correlations

2.1.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175718. The maximum correlation in this data set is 0.8869939.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902268. The maximum correlation was 0.8853661.

2.1.5 Estimating Number of Factors

2.1.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 16.

2.1.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Number of Factors	MAP value
1	0.0252
2	0.0208
3	0.0163
4	0.0147
5	0.0142
6	0.0133
7	0.0126
8	0.0121
9	0.0118
10	0.0117
11	0.0115
12	0.0113
13	0.0114
14	0.0117
15	0.0117
16	0.0121
17	0.0121
18	0.0126

2.1.6 Factor Analysis for 11 Factors

2.1.6.1 11 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 2.2247374^{4}
  
• degrees of freedom: 1529
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4676849. Should be > 0.9; need reference)

2.1.6.2 11 Factor Model Communalities

	fanal11.communality
TRAIN01	0.44
TRAIN02	0.24
TRAIN04	0.61
TRAIN05	0.32
TRAIN06	0.25
TRAIN07	0.60
TRAIN08	0.61
AGG09	0.76
AGG10	0.63
AGG11	0.76
AGG12	0.79
AGG13	0.95
AGG14	0.45
AGG15	0.76
AGG16	0.73
AGG17	0.55
AGG18	0.72
AGG19	0.59
AGG20	0.47
FEAR21	0.81
FEAR22	0.32
FEAR23	0.78
FEAR24	0.84
FEAR25	0.46
FEAR27	0.67
FEAR28	0.64
FEAR29	0.13
FEAR31	0.59
SEPR32	0.69
SEPR33	0.53
SEPR34	0.73
EXCITE35	0.48
EXCITE36	0.63
EXCITE37	0.58
EXCITE38	0.62
ATT39	0.29
ATT40	0.28
ATT41	0.32
ATT42	0.35
PLAY43	0.55
PLAY44	0.79
PLAY45	0.74
PLAY46	0.71
IMP47	0.46
IMP48	0.41
IMP49	0.39
MISC50	0.32
MISC51	0.37
MISC52	0.23
MISC54	0.58
MISC55	0.70
MISC56	0.53
MISC57	0.33
MISC58	0.23
MISC59	0.54
MISC60	0.38
MISC61	0.50
MISC62	0.48
MISC63	0.37
MISC64	0.54
MISC65	0.60
MISC66	0.69
MISC67	0.62
MISC68	0.20
MISC69	0.22
MISC70	0.33
MISC71	0.28

2.1.6.3 How many communalities < 0.40?

There are 21 items with communality < 0.40.

	fanal11.communality	item
TRAIN02	0.24	TRAIN02
TRAIN05	0.32	TRAIN05
TRAIN06	0.25	TRAIN06
FEAR22	0.32	FEAR22
FEAR29	0.13	FEAR29
ATT39	0.29	ATT39
ATT40	0.28	ATT40
ATT41	0.32	ATT41
ATT42	0.35	ATT42
IMP49	0.39	IMP49
MISC50	0.32	MISC50
MISC51	0.37	MISC51
MISC52	0.23	MISC52
MISC57	0.33	MISC57
MISC58	0.23	MISC58
MISC60	0.38	MISC60
MISC63	0.37	MISC63
MISC68	0.20	MISC68
MISC69	0.22	MISC69
MISC70	0.33	MISC70
MISC71	0.28	MISC71

2.1.6.4 11 Factor Model Loadings

	PA2	PA10	PA1	PA5	PA11	PA6	PA8	PA3	PA4	PA7	PA9
TRAIN01	-0.14	-0.12	0.17	-0.02	-0.09	0.06	0.04	0.05	0.54	-0.02	-0.02
TRAIN02	-0.04	0.06	0.14	-0.02	0.00	0.03	0.01	-0.03	0.40	0.09	-0.06
TRAIN04	-0.04	0.05	0.30	0.01	-0.02	0.05	-0.04	-0.04	0.63	0.02	-0.08
TRAIN05	0.04	-0.15	0.12	0.14	-0.06	0.00	-0.02	0.13	0.43	0.07	0.02
TRAIN06	-0.09	0.02	0.21	-0.04	0.10	0.07	0.06	-0.12	0.30	-0.03	-0.13
TRAIN07	-0.13	0.02	0.60	-0.02	-0.03	0.05	0.03	-0.07	0.27	0.00	-0.06
TRAIN08	-0.74	0.01	0.08	0.01	0.06	0.01	-0.05	-0.03	0.06	0.05	0.03
AGG09	0.05	0.29	0.07	0.06	0.03	-0.06	0.08	0.71	0.03	-0.05	0.04
AGG10	0.03	0.05	-0.04	0.06	-0.03	0.06	0.19	0.68	-0.04	0.01	-0.01
AGG11	-0.09	-0.02	-0.13	0.81	0.00	0.12	0.04	0.01	0.09	-0.12	0.07
AGG12	-0.04	0.08	0.06	0.88	0.01	-0.03	-0.01	-0.04	-0.07	0.04	-0.03
AGG13	-0.01	0.03	0.02	0.95	0.01	-0.10	-0.02	0.07	0.03	0.05	0.01
AGG14	-0.09	0.05	-0.03	-0.07	0.05	0.08	0.16	0.59	-0.01	0.06	0.08
AGG15	-0.02	0.26	0.00	0.13	0.01	-0.03	0.06	0.70	0.01	-0.02	-0.04
AGG16	0.00	-0.04	0.09	0.02	0.02	-0.03	0.75	0.25	-0.01	0.00	-0.05
AGG17	0.10	0.08	-0.01	0.17	0.21	0.22	0.08	0.36	0.08	0.12	-0.35
AGG18	0.06	-0.08	0.05	0.03	-0.03	0.02	0.75	0.27	-0.02	-0.03	0.02
AGG19	0.15	-0.11	0.06	0.29	0.02	0.13	0.57	0.09	-0.06	0.10	-0.13
AGG20	0.02	-0.13	0.01	0.48	0.02	0.12	0.41	-0.07	-0.07	0.02	-0.04
FEAR21	0.01	0.83	0.03	0.07	0.02	0.06	-0.04	0.13	0.00	0.01	-0.04
FEAR22	-0.04	0.25	0.23	0.06	0.24	0.08	0.05	-0.21	-0.11	0.05	-0.04
FEAR23	0.00	0.79	0.01	0.00	0.06	0.05	0.01	0.18	-0.01	-0.01	0.02
FEAR24	-0.08	0.83	0.03	0.06	-0.01	0.00	0.00	0.15	-0.05	0.03	0.00
FEAR25	0.02	0.28	0.21	0.12	0.35	0.03	0.02	-0.08	0.05	0.02	0.06
FEAR27	-0.04	0.45	-0.10	-0.03	0.10	-0.04	0.59	-0.18	0.11	-0.03	0.10
FEAR28	0.07	0.49	0.20	0.06	0.38	0.06	-0.02	-0.09	-0.03	0.06	-0.09
FEAR29	-0.07	0.12	0.05	0.11	0.08	0.08	0.10	-0.04	0.08	0.08	-0.02
FEAR31	-0.07	0.42	-0.04	-0.04	0.12	-0.02	0.52	-0.29	0.11	-0.01	0.09
SEPR32	0.00	0.12	0.06	-0.02	-0.07	0.81	0.05	-0.04	-0.10	0.08	-0.06
SEPR33	-0.01	-0.01	0.08	0.05	-0.01	0.69	0.00	-0.08	-0.02	0.03	0.04
SEPR34	-0.03	-0.05	-0.07	-0.06	0.10	0.82	-0.04	0.06	0.12	-0.03	0.04
EXCITE35	-0.11	0.09	0.04	-0.11	-0.10	0.16	0.01	0.02	-0.05	0.64	0.06
EXCITE36	0.20	-0.01	0.05	0.00	0.02	-0.05	-0.08	0.03	-0.01	0.73	-0.04
EXCITE37	-0.07	-0.01	-0.04	0.02	-0.02	0.03	0.03	-0.01	0.04	0.77	-0.02
EXCITE38	0.03	-0.02	-0.14	0.05	0.09	-0.04	0.01	-0.05	0.06	0.76	0.00
ATT39	-0.06	0.09	0.14	-0.13	-0.11	0.08	0.03	0.09	-0.38	0.23	0.22
ATT40	-0.20	0.07	0.29	-0.03	0.08	0.13	0.03	0.05	-0.15	0.11	0.14
ATT41	-0.06	-0.02	0.13	0.08	-0.02	0.11	0.02	-0.07	-0.21	0.12	0.45
ATT42	-0.12	-0.02	0.08	0.02	0.07	0.13	0.10	-0.01	-0.04	0.16	0.43
PLAY43	0.52	-0.25	-0.02	-0.04	0.05	-0.09	0.00	-0.30	-0.02	0.06	0.12
PLAY44	0.88	0.00	0.03	-0.01	-0.01	0.00	0.08	-0.05	0.02	0.06	-0.02
PLAY45	0.82	0.06	-0.01	-0.10	-0.03	-0.06	0.02	0.00	-0.05	0.01	0.06
PLAY46	0.77	-0.04	-0.14	-0.01	0.03	0.05	-0.06	0.10	0.07	0.04	-0.08
IMP47	0.21	0.09	-0.06	0.02	-0.01	0.04	0.05	0.00	0.43	0.17	0.29
IMP48	0.15	0.04	0.04	0.20	0.00	0.05	0.05	-0.05	0.28	0.13	0.32
IMP49	0.00	0.05	0.05	0.20	-0.02	-0.05	0.01	0.00	0.45	0.16	0.16
MISC50	0.04	0.00	-0.03	0.20	0.09	0.24	-0.06	0.02	0.20	0.08	0.21
MISC51	-0.13	-0.16	-0.01	0.02	0.02	0.28	0.01	0.11	0.35	0.05	0.17
MISC52	-0.32	-0.04	0.00	0.06	0.05	-0.07	0.05	0.00	0.05	0.11	0.34
MISC54	-0.11	0.02	0.16	0.00	0.66	-0.02	0.02	-0.04	0.00	0.08	-0.02
MISC55	0.02	-0.03	-0.04	-0.06	0.87	0.02	0.01	0.04	-0.07	0.00	0.00
MISC56	-0.03	-0.03	0.03	0.11	0.70	-0.03	-0.04	0.01	0.01	-0.04	0.03
MISC57	0.06	-0.06	0.10	0.14	-0.05	0.16	-0.01	-0.05	0.24	0.10	0.26
MISC58	0.13	-0.03	0.06	0.33	0.00	0.26	-0.04	0.00	0.04	-0.12	0.11
MISC59	0.27	0.05	0.14	0.10	-0.02	0.37	-0.08	-0.04	0.13	-0.02	0.37
MISC60	0.30	0.02	0.07	-0.04	-0.03	0.06	-0.14	0.01	-0.01	0.14	0.41
MISC61	0.43	0.01	0.04	-0.01	-0.12	0.17	-0.13	0.11	-0.06	0.16	0.30
MISC62	0.00	-0.03	0.40	-0.04	-0.01	-0.06	0.41	0.04	0.09	0.04	0.22
MISC63	-0.01	-0.02	0.35	0.04	0.11	-0.14	0.08	0.05	0.09	0.14	0.31
MISC64	-0.07	-0.14	0.66	0.00	0.06	0.05	0.02	0.07	0.08	-0.04	0.00
MISC65	-0.09	-0.12	0.62	-0.04	0.05	0.05	0.14	0.04	0.15	-0.04	0.09
MISC66	-0.05	0.21	0.63	-0.01	0.18	0.05	-0.06	0.00	0.07	-0.06	0.02
MISC67	-0.07	0.20	0.63	0.07	0.11	0.07	-0.01	-0.04	-0.06	-0.06	0.05
MISC68	0.02	-0.13	-0.09	0.10	0.31	0.07	0.00	0.12	0.19	0.05	0.08
MISC69	-0.07	-0.05	-0.07	-0.01	0.33	0.10	0.03	0.11	0.14	0.03	0.20
MISC70	0.02	-0.06	-0.05	0.07	0.08	0.14	0.08	0.19	0.08	0.00	0.43
MISC71	-0.03	-0.04	0.08	-0.05	0.26	0.10	-0.07	0.08	0.05	-0.06	0.38

2.1.6.4.1 11 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
14	PA1	0.29	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
45	PA1	0.35	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
46	PA1	0.66	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
47	PA1	0.62	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
48	PA1	0.63	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
49	PA1	0.63	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
66	PA1	0.60	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
67	PA1	0.08	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
21	PA10	0.83	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
22	PA10	0.25	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
23	PA10	0.79	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
24	PA10	0.83	FEAR24	When an unfamiliar person tries to touch or pet the dog
27	PA10	0.49	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
28	PA10	0.12	FEAR29	When having nails trimmed, or feet touched/handled
25	PA11	0.35	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
36	PA11	0.66	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
37	PA11	0.87	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
38	PA11	0.70	MISC56	Nervous or frightened when ascending or descending some types of stairs
50	PA11	0.31	MISC68	Chases own tail/hind end
51	PA11	0.33	MISC69	Chases/follows shadows, light spots, etc.
43	PA2	0.43	MISC61	Active, energetic, always on the go
54	PA2	0.52	PLAY43	Eagerly engages in play with new/unfamiliar people
55	PA2	0.88	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
56	PA2	0.82	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
57	PA2	0.77	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.71	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.68	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.59	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.70	AGG15	When an unfamiliar person tries to touch or pet the dog
9	PA3	0.36	AGG17	When stared at directly by you or another familiar person
30	PA4	0.43	IMP47	Impulsive; doesn’t seem to think before s/he acts
32	PA4	0.45	IMP49	Is difficult to interrupt or distract when doing things s/he wants to do
34	PA4	0.35	MISC51	Escapes or would escape from home, yard or kennel given the chance
61	PA4	0.54	TRAIN01	Is hard to recall when off the leash
62	PA4	0.40	TRAIN02	Is slow to obey a ‘sit’ command
63	PA4	0.63	TRAIN04	Has difficulty attending/listening to things you say or do
64	PA4	0.43	TRAIN05	Is slow to respond to corrections or reprimands: thick-skinned
65	PA4	0.30	TRAIN06	Is slow to learn new tricks or tasks
3	PA5	0.81	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA5	0.88	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA5	0.95	AGG13	When his/her food is taken away by you or another familiar person
12	PA5	0.48	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
40	PA5	0.33	MISC58	Urinates against objects/furnishings indoors
33	PA6	0.24	MISC50	NA
41	PA6	0.37	MISC59	Hyperactive, restless, has trouble settling down
58	PA6	0.81	SEPR32	Restlessness/agitation/pacing when left alone
59	PA6	0.69	SEPR33	Barking or whining when left alone
60	PA6	0.82	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
13	PA7	0.23	ATT39	Displays a strong attachment for you or another familiar person
17	PA7	0.64	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
18	PA7	0.73	EXCITE36	Excitable when playing with you or other familiar persons
19	PA7	0.77	EXCITE37	Excitable just before being taken out for a walk
20	PA7	0.76	EXCITE38	Excitable just before being taken out for work or training
8	PA8	0.75	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA8	0.75	AGG18	When barked, growled, or lunged at by another dog
11	PA8	0.57	AGG19	Towards other familiar dogs
26	PA8	0.59	FEAR27	When approached directly by an unfamiliar dog
29	PA8	0.52	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
44	PA8	0.41	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
15	PA9	0.45	ATT41	Tends to nudge or paw you (or others) for attention
16	PA9	0.43	ATT42	Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
31	PA9	0.32	IMP48	Becomes frustrated/impatient in a wide range of situations
35	PA9	0.34	MISC52	Begs persistently for food when people are eating
39	PA9	0.26	MISC57	Pulls excessively hard when on leash
42	PA9	0.41	MISC60	Playful, puppyish, boisterous
52	PA9	0.43	MISC70	Barks persistently when alarmed or excited
53	PA9	0.38	MISC71	Licks people or objects excessively

2.1.7 11 Model Reliability Measures

The overall alpha for all items is 0.8806686.

The overall omega for all items is 0.921832.

Hierarchical omega is 0.5481117.

2.2 12 Factors

2.2.1 Imputation of Missing Items (12 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.2.2 12-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.2.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.5696263^{4} with 2278 DF, p = 0e+00.

2.2.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570906

2.2.3 12-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.2.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.0101668^{4} with 2278 DF, p = 0e+00.

2.2.3.2 12-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8570906

2.2.4 Between-Item Correlations

2.2.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175318. The maximum correlation in this data set is 0.8879515.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6908209. The maximum correlation was 0.8870493.

2.2.5 Estimating Number of Factors

2.2.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 16.

2.2.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Number of Factors	MAP value
1	0.0252
2	0.0210
3	0.0162
4	0.0145
5	0.0139
6	0.0131
7	0.0125
8	0.0121
9	0.0116
10	0.0115
11	0.0109
12	0.0110
13	0.0113
14	0.0114
15	0.0115
16	0.0118
17	0.0122
18	0.0124

2.2.6 Factor Analysis for 12 Factors

2.2.6.1 12 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 2.2047631^{4}
  
• degrees of freedom: 1528
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4668955. Should be > 0.9; need reference)

2.2.6.2 12 Factor Model Communalities

	fanal12.communality
TRAIN01	0.46
TRAIN02	0.32
TRAIN03	0.41
TRAIN04	0.62
TRAIN05	0.33
TRAIN06	0.27
TRAIN07	0.61
TRAIN08	0.61
AGG09	0.75
AGG10	0.66
AGG11	0.76
AGG12	0.78
AGG13	0.96
AGG14	0.49
AGG15	0.78
AGG16	0.75
AGG17	0.58
AGG18	0.74
AGG19	0.61
AGG20	0.46
FEAR21	0.81
FEAR22	0.31
FEAR23	0.80
FEAR24	0.84
FEAR25	0.46
FEAR27	0.66
FEAR28	0.64
FEAR29	0.16
FEAR31	0.58
SEPR32	0.67
SEPR33	0.53
SEPR34	0.70
EXCITE35	0.50
EXCITE36	0.63
EXCITE37	0.57
EXCITE38	0.61
ATT39	0.29
ATT40	0.34
ATT41	0.31
ATT42	0.34
PLAY43	0.55
PLAY44	0.81
PLAY45	0.76
PLAY46	0.72
IMP47	0.47
IMP48	0.42
IMP49	0.39
MISC50	0.30
MISC51	0.35
MISC52	0.43
MISC53	0.44
MISC54	0.62
MISC55	0.73
MISC56	0.57
MISC57	0.35
MISC58	0.25
MISC59	0.55
MISC60	0.50
MISC61	0.67
MISC62	0.51
MISC63	0.38
MISC64	0.57
MISC65	0.61
MISC66	0.68
MISC67	0.60
MISC69	0.15
MISC70	0.33
MISC71	0.26

2.2.6.3 How many communalities < 0.40?

There are 18 items with communality < 0.40.

	fanal12.communality	item
TRAIN02	0.32	TRAIN02
TRAIN05	0.33	TRAIN05
TRAIN06	0.27	TRAIN06
FEAR22	0.31	FEAR22
FEAR29	0.16	FEAR29
ATT39	0.29	ATT39
ATT40	0.34	ATT40
ATT41	0.31	ATT41
ATT42	0.34	ATT42
IMP49	0.39	IMP49
MISC50	0.30	MISC50
MISC51	0.35	MISC51
MISC57	0.35	MISC57
MISC58	0.25	MISC58
MISC63	0.38	MISC63
MISC69	0.15	MISC69
MISC70	0.33	MISC70
MISC71	0.26	MISC71

2.2.6.4 12 Factor Model Loadings

	PA10	PA1	PA2	PA5	PA4	PA6	PA8	PA11	PA3	PA9	PA7	PA12
TRAIN01	-0.12	0.11	-0.10	-0.02	0.57	0.05	0.03	-0.06	0.06	-0.05	0.07	-0.02
TRAIN02	0.07	0.02	-0.04	-0.08	0.54	0.02	0.01	0.05	0.00	0.10	0.01	-0.05
TRAIN03	-0.01	-0.01	-0.10	-0.10	0.58	0.11	0.03	0.04	-0.01	0.11	0.01	0.03
TRAIN04	0.07	0.23	-0.03	0.01	0.67	0.03	-0.03	-0.02	-0.05	0.00	-0.05	-0.01
TRAIN05	-0.15	0.07	0.03	0.14	0.45	-0.02	0.02	-0.04	0.12	0.06	0.01	0.08
TRAIN06	0.02	0.16	-0.06	-0.05	0.36	0.07	0.04	0.10	-0.11	-0.02	-0.05	-0.14
TRAIN07	0.04	0.59	-0.12	0.00	0.30	0.04	0.03	-0.05	-0.09	0.00	-0.06	-0.03
TRAIN08	0.03	0.09	-0.71	0.00	0.07	0.01	-0.04	0.07	-0.03	0.05	0.06	-0.03
AGG09	0.29	0.08	0.06	0.06	0.03	-0.06	0.12	0.02	0.67	-0.06	-0.01	0.06
AGG10	0.03	-0.02	0.08	0.04	-0.04	0.08	0.18	-0.05	0.70	0.00	0.05	-0.08
AGG11	-0.01	-0.13	-0.10	0.80	0.07	0.12	0.06	0.00	0.00	-0.12	0.05	0.06
AGG12	0.08	0.04	-0.06	0.88	-0.06	-0.02	0.00	0.01	-0.04	0.05	-0.03	-0.01
AGG13	0.03	0.06	0.02	0.96	0.00	-0.09	-0.02	-0.02	0.07	0.05	0.04	-0.03
AGG14	0.04	0.04	0.01	-0.07	-0.05	0.11	0.13	0.01	0.61	0.03	0.17	-0.08
AGG15	0.26	-0.05	-0.07	0.12	0.04	-0.06	0.11	0.05	0.70	-0.02	-0.05	0.08
AGG16	-0.01	0.05	-0.04	0.00	0.02	-0.04	0.79	0.04	0.19	0.00	-0.06	-0.01
AGG17	0.04	0.09	0.21	0.23	0.03	0.24	0.04	0.14	0.38	0.10	-0.19	-0.32
AGG18	-0.06	0.02	0.02	0.01	0.00	0.02	0.78	-0.01	0.22	-0.03	0.00	0.02
AGG19	-0.09	-0.02	0.05	0.27	-0.01	0.11	0.63	0.04	0.04	0.12	-0.16	0.02
AGG20	-0.12	-0.02	0.04	0.45	-0.05	0.13	0.40	0.03	-0.06	0.02	0.04	-0.11
FEAR21	0.83	0.00	-0.01	0.08	0.01	0.05	-0.05	0.03	0.13	0.01	-0.04	0.00
FEAR22	0.24	0.17	-0.06	0.03	-0.04	0.08	0.02	0.27	-0.18	0.07	0.00	-0.06
FEAR23	0.81	0.01	-0.02	0.01	0.00	0.05	0.01	0.05	0.16	-0.01	-0.04	0.05
FEAR24	0.85	0.01	-0.10	0.07	-0.04	0.00	-0.01	-0.01	0.12	0.03	-0.01	0.02
FEAR25	0.29	0.24	0.07	0.13	0.05	0.05	-0.02	0.31	-0.08	0.01	0.07	-0.05
FEAR27	0.47	-0.03	0.04	-0.01	0.03	-0.03	0.53	0.06	-0.21	-0.04	0.20	-0.11
FEAR28	0.47	0.16	0.07	0.05	0.01	0.07	-0.05	0.40	-0.06	0.07	-0.06	-0.09
FEAR29	0.11	0.07	0.02	0.09	0.08	0.10	0.04	0.06	0.01	0.07	0.13	-0.18
FEAR31	0.42	0.01	0.03	-0.04	0.05	0.01	0.43	0.09	-0.28	-0.03	0.23	-0.16
SEPR32	0.11	0.03	-0.02	-0.03	-0.06	0.80	0.04	-0.06	-0.02	0.09	-0.08	-0.01
SEPR33	-0.01	0.05	-0.03	0.03	0.02	0.69	0.00	0.00	-0.07	0.03	0.02	0.04
SEPR34	-0.05	-0.03	-0.01	-0.04	0.08	0.81	-0.05	0.07	0.06	-0.05	0.05	0.03
EXCITE35	0.10	0.01	-0.15	-0.12	-0.01	0.14	0.05	-0.09	0.00	0.64	0.01	0.11
EXCITE36	-0.02	0.05	0.17	0.02	0.00	-0.06	-0.06	0.02	0.02	0.72	-0.05	0.05
EXCITE37	-0.02	-0.05	-0.07	0.03	0.04	0.03	0.04	-0.01	-0.01	0.75	0.02	0.02
EXCITE38	-0.03	-0.13	0.06	0.06	0.05	-0.03	0.00	0.09	-0.05	0.74	0.05	-0.02
ATT39	0.10	0.20	-0.01	-0.15	-0.36	0.12	0.00	-0.14	0.10	0.23	0.17	0.02
ATT40	0.06	0.41	-0.06	-0.02	-0.18	0.18	-0.04	0.00	0.08	0.10	0.20	-0.15
ATT41	0.00	0.22	0.03	0.05	-0.23	0.16	-0.01	-0.06	-0.06	0.10	0.37	0.10
ATT42	0.01	0.18	-0.04	0.01	-0.09	0.17	0.08	0.02	-0.03	0.13	0.35	0.14
PLAY43	-0.24	-0.01	0.49	-0.03	-0.05	-0.09	-0.01	0.03	-0.30	0.06	0.06	0.11
PLAY44	-0.01	0.03	0.87	-0.01	0.02	0.01	0.06	-0.03	-0.04	0.06	-0.05	0.03
PLAY45	0.03	0.00	0.83	-0.09	-0.08	-0.05	-0.02	-0.05	0.03	0.01	0.05	0.05
PLAY46	-0.07	-0.15	0.76	0.00	0.05	0.04	-0.08	0.02	0.12	0.03	-0.06	0.01
IMP47	0.09	-0.05	0.30	0.01	0.38	0.06	0.01	-0.01	0.03	0.12	0.33	0.09
IMP48	0.04	0.05	0.23	0.17	0.24	0.07	0.01	0.01	-0.01	0.10	0.34	0.09
IMP49	0.04	0.09	0.11	0.20	0.40	-0.04	-0.02	-0.05	0.02	0.13	0.24	-0.03
MISC50	0.01	0.05	0.09	0.22	0.13	0.26	-0.05	0.05	-0.01	0.05	0.14	0.12
MISC51	-0.15	0.02	-0.09	0.04	0.28	0.27	0.01	0.00	0.11	0.01	0.20	0.10
MISC52	-0.07	0.02	-0.18	0.03	0.00	-0.05	-0.06	0.06	0.12	0.07	0.61	-0.06
MISC53	-0.13	-0.08	-0.15	0.19	0.15	0.04	-0.09	-0.01	0.02	0.02	0.54	0.01
MISC54	-0.01	0.16	-0.04	-0.01	0.01	-0.01	-0.02	0.69	0.00	0.07	0.09	-0.14
MISC55	-0.02	-0.07	-0.02	-0.08	-0.04	0.02	0.04	0.89	0.02	0.01	-0.04	0.04
MISC56	-0.03	-0.01	-0.06	0.10	0.02	-0.04	-0.01	0.74	0.01	-0.04	0.00	0.06
MISC57	-0.04	0.05	0.00	0.13	0.25	0.14	0.03	0.00	-0.06	0.09	0.15	0.27
MISC58	-0.04	-0.01	0.05	0.32	0.06	0.24	0.00	0.06	-0.01	-0.11	0.00	0.20
MISC59	0.06	0.11	0.18	0.09	0.11	0.35	-0.02	0.03	-0.06	-0.02	0.15	0.40
MISC60	0.06	0.03	0.11	-0.05	-0.01	0.01	-0.02	0.03	-0.06	0.14	0.04	0.60
MISC61	0.04	-0.02	0.19	-0.02	-0.05	0.12	0.01	-0.04	0.03	0.18	-0.10	0.64
MISC62	-0.01	0.39	-0.06	-0.04	0.07	-0.09	0.46	0.02	-0.02	0.03	0.09	0.22
MISC63	-0.01	0.38	-0.02	0.04	0.06	-0.14	0.10	0.12	0.03	0.12	0.20	0.22
MISC64	-0.15	0.72	-0.05	0.04	0.06	0.05	0.02	0.01	0.06	-0.05	-0.03	-0.01
MISC65	-0.11	0.65	-0.06	-0.01	0.15	0.04	0.13	0.03	0.02	-0.06	0.07	0.02
MISC66	0.20	0.61	-0.05	-0.01	0.10	0.04	-0.08	0.18	0.01	-0.06	0.01	0.00
MISC67	0.19	0.58	-0.10	0.06	-0.01	0.07	-0.01	0.14	-0.02	-0.05	0.00	0.03
MISC69	0.00	0.06	-0.01	0.03	0.04	0.12	0.04	0.21	0.04	0.00	0.13	0.08
MISC70	-0.05	-0.02	0.02	0.05	0.03	0.15	0.10	0.12	0.18	-0.02	0.31	0.27
MISC71	-0.01	0.19	0.04	-0.04	-0.02	0.13	-0.07	0.20	0.05	-0.09	0.28	0.15

2.2.6.4.1 12 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
14	PA1	0.41	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
46	PA1	0.38	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
47	PA1	0.72	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
48	PA1	0.65	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
49	PA1	0.61	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
50	PA1	0.58	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
67	PA1	0.59	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
68	PA1	0.09	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
21	PA10	0.83	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
23	PA10	0.81	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
24	PA10	0.85	FEAR24	When an unfamiliar person tries to touch or pet the dog
27	PA10	0.47	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
22	PA11	0.27	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
25	PA11	0.31	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
37	PA11	0.69	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38	PA11	0.89	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
39	PA11	0.74	MISC56	Nervous or frightened when ascending or descending some types of stairs
51	PA11	0.21	MISC69	Chases/follows shadows, light spots, etc.
40	PA12	0.27	MISC57	Pulls excessively hard when on leash
42	PA12	0.40	MISC59	Hyperactive, restless, has trouble settling down
43	PA12	0.60	MISC60	Playful, puppyish, boisterous
44	PA12	0.64	MISC61	Active, energetic, always on the go
54	PA2	0.49	PLAY43	Eagerly engages in play with new/unfamiliar people
55	PA2	0.87	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
56	PA2	0.83	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
57	PA2	0.76	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.67	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.70	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.61	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.70	AGG15	When an unfamiliar person tries to touch or pet the dog
9	PA3	0.38	AGG17	When stared at directly by you or another familiar person
30	PA4	0.38	IMP47	Impulsive; doesn’t seem to think before s/he acts
32	PA4	0.40	IMP49	Is difficult to interrupt or distract when doing things s/he wants to do
34	PA4	0.28	MISC51	Escapes or would escape from home, yard or kennel given the chance
61	PA4	0.57	TRAIN01	Is hard to recall when off the leash
62	PA4	0.54	TRAIN02	Is slow to obey a ‘sit’ command
63	PA4	0.58	TRAIN03	Is slow to obey a ‘stay’ command
64	PA4	0.67	TRAIN04	Has difficulty attending/listening to things you say or do
65	PA4	0.45	TRAIN05	Is slow to respond to corrections or reprimands: thick-skinned
66	PA4	0.36	TRAIN06	Is slow to learn new tricks or tasks
3	PA5	0.80	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA5	0.88	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA5	0.96	AGG13	When his/her food is taken away by you or another familiar person
12	PA5	0.45	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
41	PA5	0.32	MISC58	Urinates against objects/furnishings indoors
33	PA6	0.26	MISC50	NA
58	PA6	0.80	SEPR32	Restlessness/agitation/pacing when left alone
59	PA6	0.69	SEPR33	Barking or whining when left alone
60	PA6	0.81	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
15	PA7	0.37	ATT41	Tends to nudge or paw you (or others) for attention
16	PA7	0.35	ATT42	Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
28	PA7	0.13	FEAR29	When having nails trimmed, or feet touched/handled
31	PA7	0.34	IMP48	Becomes frustrated/impatient in a wide range of situations
35	PA7	0.61	MISC52	Begs persistently for food when people are eating
36	PA7	0.54	MISC53	Steals food
52	PA7	0.31	MISC70	Barks persistently when alarmed or excited
53	PA7	0.28	MISC71	Licks people or objects excessively
8	PA8	0.79	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA8	0.78	AGG18	When barked, growled, or lunged at by another dog
11	PA8	0.63	AGG19	Towards other familiar dogs
26	PA8	0.53	FEAR27	When approached directly by an unfamiliar dog
29	PA8	0.43	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
45	PA8	0.46	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
13	PA9	0.23	ATT39	Displays a strong attachment for you or another familiar person
17	PA9	0.64	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
18	PA9	0.72	EXCITE36	Excitable when playing with you or other familiar persons
19	PA9	0.75	EXCITE37	Excitable just before being taken out for a walk
20	PA9	0.74	EXCITE38	Excitable just before being taken out for work or training

2.2.7 12 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.884123.

The overall omega for all items is 0.9258431.

Hierarchical omega is 0.5616952.

2.3 13 Factors

2.3.1 Imputation of Missing Items (13 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.3.2 13-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.3.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.7613184^{4} with 2415 DF, p = 0e+00.

2.3.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8576926

2.3.3 13-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.3.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.1941027^{4} with 2415 DF, p = 0e+00.

2.3.3.2 13-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8576926

2.3.4 Between-Item Correlations

2.3.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.717518. The maximum correlation in this data set is 0.8872086.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6908064. The maximum correlation was 0.8850145.

2.3.5 Estimating Number of Factors

2.3.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 16.

2.3.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Number of Factors	MAP value
1	0.0244
2	0.0205
3	0.0158
4	0.0142
5	0.0135
6	0.0127
7	0.0121
8	0.0118
9	0.0115
10	0.0114
11	0.0111
12	0.0107
13	0.0109
14	0.0111
15	0.0113
16	0.0115
17	0.0118
18	0.0119

2.3.6 Factor Analysis for 13 Factors

2.3.6.1 13 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 2.2297571^{4}
  
• degrees of freedom: 1583
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4646876. Should be > 0.9; need reference)

2.3.6.2 13 Factor Model Communalities

	fanal13.communality
TRAIN01	0.46
TRAIN02	0.38
TRAIN03	0.50
TRAIN04	0.62
TRAIN05	0.34
TRAIN06	0.27
TRAIN07	0.61
TRAIN08	0.60
AGG09	0.74
AGG10	0.65
AGG11	0.75
AGG12	0.79
AGG13	0.95
AGG14	0.48
AGG15	0.77
AGG16	0.77
AGG17	0.79
AGG18	0.73
AGG19	0.62
AGG20	0.48
FEAR21	0.80
FEAR22	0.32
FEAR23	0.80
FEAR24	0.86
FEAR25	0.45
FEAR26	0.44
FEAR27	0.74
FEAR28	0.66
FEAR29	0.46
FEAR30	0.56
FEAR31	0.63
SEPR32	0.67
SEPR33	0.54
SEPR34	0.73
EXCITE35	0.50
EXCITE36	0.62
EXCITE37	0.59
EXCITE38	0.63
ATT39	0.29
ATT40	0.30
ATT41	0.30
ATT42	0.33
PLAY43	0.55
PLAY44	0.79
PLAY45	0.75
PLAY46	0.70
IMP47	0.45
IMP48	0.42
IMP49	0.39
MISC50	0.34
MISC51	0.39
MISC52	0.44
MISC53	0.45
MISC54	0.62
MISC55	0.75
MISC56	0.54
MISC57	0.34
MISC58	0.25
MISC59	0.55
MISC60	0.40
MISC61	0.54
MISC62	0.48
MISC63	0.38
MISC64	0.59
MISC65	0.63
MISC66	0.67
MISC67	0.59
MISC69	0.24
MISC70	0.34
MISC71	0.28

2.3.6.3 How many communalities < 0.40?

There are 18 items with communality < 0.40.

	fanal13.communality	item
TRAIN02	0.38	TRAIN02
TRAIN05	0.34	TRAIN05
TRAIN06	0.27	TRAIN06
FEAR22	0.32	FEAR22
ATT39	0.29	ATT39
ATT40	0.30	ATT40
ATT41	0.30	ATT41
ATT42	0.33	ATT42
IMP49	0.39	IMP49
MISC50	0.34	MISC50
MISC51	0.39	MISC51
MISC57	0.34	MISC57
MISC58	0.25	MISC58
MISC60	0.40	MISC60
MISC63	0.38	MISC63
MISC69	0.24	MISC69
MISC70	0.34	MISC70
MISC71	0.28	MISC71

2.3.6.4 13 Factor Model Loadings

	PA12	PA2	PA1	PA4	PA6	PA13	PA8	PA5	PA9	PA3	PA11	PA10	PA7
TRAIN01	-0.13	-0.09	0.16	-0.02	0.04	0.53	0.00	-0.10	-0.05	0.05	0.14	0.05	-0.11
TRAIN02	0.05	-0.04	-0.03	-0.08	-0.01	0.59	0.03	0.07	0.06	0.03	-0.08	0.13	0.07
TRAIN03	-0.03	-0.07	-0.05	-0.09	0.10	0.66	0.06	0.06	0.07	0.03	-0.09	0.10	0.15
TRAIN04	0.08	-0.04	0.24	0.03	0.02	0.65	-0.02	-0.01	0.00	-0.07	0.00	-0.06	-0.07
TRAIN05	-0.12	0.04	0.09	0.17	-0.02	0.45	0.04	-0.02	0.06	0.10	0.05	-0.13	0.00
TRAIN06	0.02	-0.11	0.12	-0.05	0.04	0.37	0.07	0.14	-0.04	-0.12	-0.08	0.02	-0.04
TRAIN07	0.04	-0.13	0.60	-0.01	0.02	0.28	0.02	-0.05	-0.01	-0.10	-0.08	0.03	-0.03
TRAIN08	0.04	-0.71	0.11	0.01	0.01	0.07	-0.06	0.05	0.04	-0.03	0.06	0.02	0.00
AGG09	0.33	0.07	0.09	0.07	-0.05	0.03	0.16	0.03	-0.06	0.62	0.02	-0.05	-0.08
AGG10	0.06	0.05	-0.05	0.02	0.06	-0.03	0.24	-0.04	-0.01	0.66	0.02	0.07	-0.10
AGG11	0.00	-0.08	-0.10	0.80	0.14	0.05	0.05	-0.03	-0.11	-0.01	0.10	0.02	-0.04
AGG12	0.08	-0.09	0.02	0.87	-0.04	-0.04	0.04	0.04	0.06	-0.04	-0.08	-0.03	0.02
AGG13	0.03	0.01	0.05	0.94	-0.10	-0.01	-0.01	-0.02	0.05	0.07	0.01	0.08	-0.04
AGG14	0.07	-0.06	0.03	-0.07	0.09	-0.06	0.18	0.02	0.05	0.56	0.15	0.00	-0.09
AGG15	0.30	-0.01	-0.04	0.12	-0.04	0.05	0.14	0.03	-0.05	0.66	-0.03	0.03	-0.05
AGG16	0.00	-0.04	0.05	0.00	-0.05	0.04	0.82	0.06	0.00	0.16	-0.04	-0.03	0.00
AGG17	0.04	0.12	0.12	0.17	0.20	-0.07	0.01	0.08	0.13	0.26	-0.02	0.08	-0.65
AGG18	-0.05	0.04	0.04	0.02	0.02	0.01	0.79	-0.01	-0.03	0.19	0.03	0.00	0.00
AGG19	-0.09	0.09	-0.02	0.27	0.11	0.01	0.64	0.04	0.09	0.04	-0.15	0.05	-0.01
AGG20	-0.16	0.00	-0.05	0.44	0.09	-0.03	0.43	0.05	0.00	-0.04	-0.06	0.15	0.06
FEAR21	0.82	-0.01	0.00	0.08	0.04	0.01	-0.06	0.04	0.01	0.10	-0.02	0.06	-0.03
FEAR22	0.20	-0.08	0.13	0.02	0.05	-0.01	0.03	0.30	0.05	-0.14	-0.11	0.13	0.10
FEAR23	0.82	-0.02	0.01	0.01	0.05	0.00	0.02	0.07	0.00	0.13	-0.01	-0.04	0.00
FEAR24	0.86	-0.10	0.00	0.06	-0.01	-0.03	-0.02	-0.01	0.04	0.11	-0.01	0.05	0.02
FEAR25	0.29	0.02	0.23	0.12	0.03	0.04	-0.01	0.33	0.03	-0.10	0.05	0.01	-0.01
FEAR26	0.36	0.08	0.00	0.09	0.08	0.04	0.00	-0.01	-0.02	0.04	-0.01	0.43	0.01
FEAR27	0.46	-0.01	0.01	-0.03	-0.05	-0.03	0.48	0.02	-0.01	-0.28	0.32	0.08	-0.13
FEAR28	0.46	0.06	0.13	0.03	0.03	0.02	-0.06	0.40	0.04	-0.07	-0.10	0.18	-0.04
FEAR29	0.00	0.05	0.04	0.03	0.06	0.07	-0.03	-0.01	0.00	0.05	0.03	0.65	-0.05
FEAR30	-0.01	0.09	0.06	0.13	0.12	0.03	0.01	0.13	-0.05	-0.03	0.00	0.62	-0.03
FEAR31	0.37	-0.03	0.03	-0.08	-0.02	-0.01	0.37	0.06	0.00	-0.33	0.30	0.17	-0.11
SEPR32	0.10	-0.04	0.01	-0.05	0.79	-0.04	0.06	-0.04	0.08	-0.02	-0.13	0.08	0.00
SEPR33	-0.02	-0.03	0.02	0.02	0.69	0.05	0.02	0.01	0.02	-0.04	-0.07	0.10	0.09
SEPR34	-0.04	-0.03	-0.01	-0.05	0.83	0.05	-0.05	0.06	-0.03	0.02	0.11	0.00	-0.13
EXCITE35	0.11	-0.12	0.01	-0.11	0.16	0.01	0.05	-0.09	0.65	0.02	-0.04	-0.01	0.10
EXCITE36	-0.01	0.20	0.04	0.01	-0.06	0.00	-0.06	0.01	0.72	0.02	-0.09	0.04	-0.01
EXCITE37	-0.01	-0.07	-0.03	0.03	0.02	0.03	0.03	-0.02	0.79	-0.03	0.02	-0.05	-0.05
EXCITE38	-0.03	0.04	-0.12	0.05	-0.04	0.03	-0.01	0.08	0.77	-0.07	0.07	-0.01	-0.08
ATT39	0.09	-0.04	0.15	-0.17	0.11	-0.31	0.03	-0.11	0.24	0.14	-0.01	0.10	0.22
ATT40	0.06	-0.17	0.36	-0.05	0.14	-0.17	-0.01	0.03	0.12	0.07	0.07	0.12	0.01
ATT41	-0.03	0.00	0.19	0.05	0.15	-0.18	0.01	-0.01	0.13	0.01	0.17	0.08	0.34
ATT42	0.00	-0.04	0.19	0.02	0.18	-0.07	0.08	0.05	0.17	0.01	0.23	0.05	0.25
PLAY43	-0.26	0.52	0.00	-0.03	-0.08	-0.06	-0.03	0.03	0.07	-0.27	0.06	-0.01	0.09
PLAY44	-0.03	0.87	0.00	-0.03	-0.01	0.01	0.07	-0.02	0.06	-0.04	-0.05	0.04	-0.03
PLAY45	0.02	0.83	-0.01	-0.11	-0.07	-0.09	-0.02	-0.05	0.02	0.03	0.04	0.04	0.01
PLAY46	-0.05	0.75	-0.16	-0.02	0.03	0.04	-0.06	0.01	0.04	0.09	-0.02	-0.03	-0.11
IMP47	0.07	0.30	-0.02	0.03	0.06	0.35	0.00	0.00	0.15	0.04	0.30	0.05	0.09
IMP48	0.02	0.22	0.05	0.18	0.07	0.25	0.02	0.03	0.12	0.02	0.23	0.08	0.20
IMP49	0.04	0.08	0.10	0.20	-0.05	0.36	-0.04	-0.06	0.14	0.00	0.24	0.08	-0.03
MISC50	0.04	0.09	0.08	0.26	0.28	0.09	-0.07	0.05	0.09	-0.06	0.21	-0.15	-0.05
MISC51	-0.13	-0.09	0.10	0.06	0.30	0.22	-0.02	-0.03	0.06	0.08	0.30	-0.11	-0.09
MISC52	-0.13	-0.24	0.02	0.01	-0.07	0.00	-0.08	0.05	0.09	0.17	0.45	0.28	0.19
MISC53	-0.17	-0.19	-0.07	0.19	0.03	0.14	-0.11	-0.02	0.04	0.07	0.43	0.19	0.18
MISC54	-0.03	-0.08	0.14	-0.03	-0.04	0.00	-0.03	0.67	0.06	0.00	0.04	0.15	-0.06
MISC55	-0.02	0.00	-0.09	-0.07	0.03	-0.01	0.05	0.91	0.00	0.02	-0.03	-0.04	0.02
MISC56	-0.02	-0.03	0.02	0.11	-0.03	0.02	-0.02	0.71	-0.04	0.00	0.04	-0.02	-0.02
MISC57	-0.04	0.09	0.10	0.15	0.18	0.25	0.01	-0.01	0.11	-0.03	0.16	-0.06	0.16
MISC58	-0.01	0.10	0.02	0.34	0.28	0.06	0.00	0.06	-0.09	-0.01	0.06	-0.14	0.05
MISC59	0.08	0.30	0.15	0.12	0.42	0.12	-0.05	0.02	0.00	-0.02	0.15	-0.06	0.25
MISC60	0.07	0.34	0.11	-0.01	0.13	0.02	-0.07	0.00	0.15	0.02	0.07	-0.11	0.34
MISC61	0.08	0.43	0.05	0.02	0.23	-0.02	-0.02	-0.07	0.18	0.09	-0.02	-0.19	0.29
MISC62	0.00	0.03	0.45	-0.03	-0.05	0.05	0.40	-0.01	0.05	-0.01	0.14	-0.02	0.10
MISC63	-0.01	0.05	0.44	0.06	-0.11	0.03	0.07	0.10	0.15	0.04	0.21	-0.02	0.12
MISC64	-0.13	-0.06	0.76	0.02	0.04	0.02	0.00	-0.01	-0.04	0.03	-0.02	0.02	-0.09
MISC65	-0.10	-0.06	0.69	-0.03	0.04	0.11	0.11	0.00	-0.04	0.00	0.08	0.05	-0.04
MISC66	0.20	-0.06	0.60	-0.01	0.03	0.10	-0.07	0.19	-0.07	0.01	-0.05	0.07	0.04
MISC67	0.19	-0.10	0.56	0.05	0.06	0.00	0.00	0.17	-0.06	0.00	-0.07	0.05	0.09
MISC69	0.04	-0.03	0.11	0.06	0.14	-0.01	0.03	0.23	0.07	-0.01	0.25	-0.22	-0.09
MISC70	-0.03	0.08	0.01	0.08	0.19	0.04	0.10	0.12	0.01	0.20	0.30	-0.07	0.22
MISC71	0.00	0.05	0.24	-0.03	0.16	-0.06	-0.11	0.19	-0.04	0.05	0.32	-0.06	0.06

2.3.6.4.1 13 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
14	PA1	0.36	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
47	PA1	0.45	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
48	PA1	0.44	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
49	PA1	0.76	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
50	PA1	0.69	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
51	PA1	0.60	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
52	PA1	0.56	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
69	PA1	0.60	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
70	PA1	0.11	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
26	PA10	0.43	FEAR26	When examined/treated by a veterinarian
29	PA10	0.65	FEAR29	When having nails trimmed, or feet touched/handled
30	PA10	0.62	FEAR30	When groomed or bathed
36	PA11	0.30	MISC51	Escapes or would escape from home, yard or kennel given the chance
37	PA11	0.45	MISC52	Begs persistently for food when people are eating
38	PA11	0.43	MISC53	Steals food
53	PA11	0.25	MISC69	Chases/follows shadows, light spots, etc.
54	PA11	0.30	MISC70	Barks persistently when alarmed or excited
55	PA11	0.32	MISC71	Licks people or objects excessively
21	PA12	0.82	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
23	PA12	0.82	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
24	PA12	0.86	FEAR24	When an unfamiliar person tries to touch or pet the dog
28	PA12	0.46	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
31	PA12	0.37	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
32	PA13	0.35	IMP47	Impulsive; doesn’t seem to think before s/he acts
33	PA13	0.25	IMP48	Becomes frustrated/impatient in a wide range of situations
34	PA13	0.36	IMP49	Is difficult to interrupt or distract when doing things s/he wants to do
42	PA13	0.25	MISC57	Pulls excessively hard when on leash
63	PA13	0.53	TRAIN01	Is hard to recall when off the leash
64	PA13	0.59	TRAIN02	Is slow to obey a ‘sit’ command
65	PA13	0.66	TRAIN03	Is slow to obey a ‘stay’ command
66	PA13	0.65	TRAIN04	Has difficulty attending/listening to things you say or do
67	PA13	0.45	TRAIN05	Is slow to respond to corrections or reprimands: thick-skinned
68	PA13	0.37	TRAIN06	Is slow to learn new tricks or tasks
46	PA2	0.43	MISC61	Active, energetic, always on the go
56	PA2	0.52	PLAY43	Eagerly engages in play with new/unfamiliar people
57	PA2	0.87	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
58	PA2	0.83	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
59	PA2	0.75	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.62	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.66	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.56	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.66	AGG15	When an unfamiliar person tries to touch or pet the dog
9	PA3	0.26	AGG17	When stared at directly by you or another familiar person
3	PA4	0.80	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.87	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.94	AGG13	When his/her food is taken away by you or another familiar person
12	PA4	0.44	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
43	PA4	0.34	MISC58	Urinates against objects/furnishings indoors
22	PA5	0.30	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
25	PA5	0.33	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
39	PA5	0.67	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
40	PA5	0.91	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
41	PA5	0.71	MISC56	Nervous or frightened when ascending or descending some types of stairs
35	PA6	0.28	MISC50	NA
44	PA6	0.42	MISC59	Hyperactive, restless, has trouble settling down
60	PA6	0.79	SEPR32	Restlessness/agitation/pacing when left alone
61	PA6	0.69	SEPR33	Barking or whining when left alone
62	PA6	0.83	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
15	PA7	0.34	ATT41	Tends to nudge or paw you (or others) for attention
16	PA7	0.25	ATT42	Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
45	PA7	0.34	MISC60	Playful, puppyish, boisterous
8	PA8	0.82	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA8	0.79	AGG18	When barked, growled, or lunged at by another dog
11	PA8	0.64	AGG19	Towards other familiar dogs
27	PA8	0.48	FEAR27	When approached directly by an unfamiliar dog
13	PA9	0.24	ATT39	Displays a strong attachment for you or another familiar person
17	PA9	0.65	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
18	PA9	0.72	EXCITE36	Excitable when playing with you or other familiar persons
19	PA9	0.79	EXCITE37	Excitable just before being taken out for a walk
20	PA9	0.77	EXCITE38	Excitable just before being taken out for work or training

2.3.7 13 Model Reliability Measures

The overall alpha for all items is 0.8884139.

The overall omega for all items is 0.9288948.

Hierarchical omega is 0.5686546.

2.4 14 Factors

2.4.1 Imputation of Missing Items (14 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.4.2 14-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.4.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.5549798^{4} with 2278 DF, p = 0e+00.

2.4.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8563417

2.4.3 14-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.4.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.0057354^{4} with 2278 DF, p = 0e+00.

2.4.3.2 14-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8563417

2.4.4 Between-Item Correlations

2.4.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175082. The maximum correlation in this data set is 0.8881154.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902317. The maximum correlation was 0.8871507.

2.4.5 Estimating Number of Factors

2.4.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 16.

2.4.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Number of Factors	MAP value
1	0.0247
2	0.0208
3	0.0162
4	0.0147
5	0.0139
6	0.0130
7	0.0124
8	0.0120
9	0.0117
10	0.0116
11	0.0112
12	0.0109
13	0.0111
14	0.0114
15	0.0116
16	0.0119
17	0.0122
18	0.0125

2.4.6 Factor Analysis for 14 Factors

2.4.6.1 14 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 2.0575826^{4}
  
• degrees of freedom: 1417
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4621591. Should be > 0.9; need reference)

2.4.6.2 14 Factor Model Communalities

	fanal14.communality
TRAIN01	0.41
TRAIN02	0.27
TRAIN04	0.63
TRAIN05	0.35
TRAIN06	0.27
TRAIN07	0.61
TRAIN08	0.63
AGG09	0.76
AGG10	0.66
AGG11	0.78
AGG12	0.78
AGG13	0.96
AGG14	0.50
AGG15	0.80
AGG16	0.74
AGG17	0.63
AGG18	0.72
AGG19	0.69
AGG20	0.60
FEAR21	0.82
FEAR22	0.39
FEAR23	0.80
FEAR24	0.86
FEAR25	0.49
FEAR26	0.44
FEAR27	0.82
FEAR28	0.67
FEAR29	0.52
FEAR30	0.57
FEAR31	0.70
SEPR32	0.68
SEPR33	0.53
SEPR34	0.71
EXCITE35	0.50
EXCITE36	0.62
EXCITE37	0.60
EXCITE38	0.62
ATT39	0.34
ATT40	0.40
ATT41	0.39
ATT42	0.36
PLAY43	0.55
PLAY44	0.82
PLAY45	0.75
PLAY46	0.71
IMP47	0.49
IMP48	0.45
IMP49	0.40
MISC50	0.35
MISC52	0.43
MISC53	0.42
MISC54	0.62
MISC55	0.72
MISC56	0.59
MISC57	0.35
MISC58	0.26
MISC59	0.57
MISC60	0.54
MISC61	0.68
MISC62	0.53
MISC63	0.38
MISC64	0.58
MISC65	0.61
MISC66	0.67
MISC67	0.58
MISC69	0.22
MISC70	0.36
MISC71	0.27

2.4.6.3 How many communalities < 0.40?

There are 16 items with communality < 0.40.

	fanal14.communality	item
TRAIN02	0.27	TRAIN02
TRAIN05	0.35	TRAIN05
TRAIN06	0.27	TRAIN06
FEAR22	0.39	FEAR22
ATT39	0.34	ATT39
ATT40	0.40	ATT40
ATT41	0.39	ATT41
ATT42	0.36	ATT42
IMP49	0.40	IMP49
MISC50	0.35	MISC50
MISC57	0.35	MISC57
MISC58	0.26	MISC58
MISC63	0.38	MISC63
MISC69	0.22	MISC69
MISC70	0.36	MISC70
MISC71	0.27	MISC71

2.4.6.4 14 Factor Model Loadings

	PA2	PA11	PA1	PA4	PA3	PA6	PA5	PA12	PA9	PA8	PA14	PA7	PA10	PA13
TRAIN01	-0.14	-0.14	0.17	-0.02	0.06	0.04	-0.08	0.50	-0.03	0.01	0.00	-0.04	0.12	0.03
TRAIN02	-0.06	0.03	0.06	-0.08	0.01	0.04	0.03	0.46	0.09	0.00	0.01	-0.03	0.11	-0.02
TRAIN04	-0.06	0.07	0.26	0.01	-0.05	0.07	-0.02	0.66	0.03	-0.02	0.02	-0.08	-0.04	-0.05
TRAIN05	0.02	-0.09	0.10	0.14	0.10	0.01	-0.03	0.48	0.07	0.06	-0.08	0.03	-0.11	0.01
TRAIN06	-0.06	-0.01	0.19	-0.04	-0.08	0.10	0.10	0.32	-0.01	-0.01	0.10	-0.06	-0.03	-0.17
TRAIN07	-0.14	0.07	0.58	-0.02	-0.10	0.04	-0.05	0.30	0.00	0.05	-0.01	-0.04	0.05	-0.03
TRAIN08	-0.73	-0.01	0.10	0.03	-0.01	0.02	0.06	0.03	0.05	-0.11	0.07	-0.01	0.04	0.00
AGG09	0.07	0.25	0.12	0.11	0.71	-0.04	0.03	0.00	-0.05	0.01	0.03	-0.01	-0.05	0.02
AGG10	0.06	0.01	-0.03	0.04	0.74	0.08	-0.04	-0.04	0.00	0.12	-0.02	0.02	0.05	-0.04
AGG11	-0.10	-0.05	-0.10	0.81	0.01	0.12	-0.02	0.04	-0.11	0.05	0.06	0.00	0.05	0.07
AGG12	-0.06	0.09	0.03	0.86	-0.04	-0.03	0.03	-0.04	0.06	0.06	0.00	0.00	-0.06	-0.05
AGG13	0.01	0.03	0.04	0.93	0.07	-0.10	-0.02	0.01	0.05	0.03	-0.02	0.01	0.08	-0.01
AGG14	-0.02	0.06	-0.01	-0.08	0.63	0.10	0.03	0.02	0.04	0.12	-0.03	0.17	-0.04	-0.10
AGG15	-0.08	0.27	-0.05	0.09	0.70	-0.06	0.04	0.03	-0.04	0.11	-0.10	-0.08	0.10	0.12
AGG16	-0.02	-0.06	0.09	-0.03	0.28	-0.05	0.03	0.01	0.00	0.60	0.30	-0.03	-0.07	-0.02
AGG17	0.19	-0.01	0.10	0.24	0.41	0.25	0.13	-0.02	0.13	-0.03	0.04	-0.28	0.11	-0.26
AGG18	0.04	-0.10	0.05	-0.03	0.30	0.00	-0.02	0.00	-0.03	0.60	0.28	0.02	-0.04	0.01
AGG19	0.07	-0.01	0.00	0.17	0.03	0.06	0.03	-0.02	0.09	0.71	0.02	-0.08	0.06	0.04
AGG20	0.03	0.00	-0.07	0.31	-0.12	0.06	0.02	0.02	-0.02	0.61	-0.09	0.14	0.10	-0.12
FEAR21	-0.01	0.80	-0.01	0.07	0.11	0.03	0.02	0.01	0.01	-0.03	0.10	-0.02	0.07	0.00
FEAR22	-0.08	0.35	0.10	-0.07	-0.25	0.02	0.28	0.00	0.03	0.22	-0.11	0.09	0.11	-0.05
FEAR23	-0.02	0.78	-0.01	0.00	0.16	0.04	0.05	0.01	-0.01	0.00	0.13	0.00	-0.05	0.02
FEAR24	-0.10	0.80	-0.01	0.07	0.14	-0.02	-0.03	-0.05	0.03	-0.05	0.16	0.00	0.03	0.02
FEAR25	0.06	0.35	0.20	0.10	-0.12	0.03	0.32	0.10	0.01	0.06	0.03	0.13	-0.02	-0.09
FEAR26	0.04	0.33	-0.01	0.06	0.04	0.06	-0.02	0.01	-0.01	0.02	0.10	0.00	0.43	0.03
FEAR27	0.01	0.16	-0.03	0.03	-0.04	-0.01	0.02	0.00	-0.01	0.08	0.82	-0.01	0.02	-0.01
FEAR28	0.06	0.49	0.12	0.00	-0.09	0.04	0.38	0.01	0.05	0.01	0.03	-0.04	0.17	-0.05
FEAR29	0.01	-0.04	0.04	0.00	0.06	0.05	-0.02	0.00	0.02	-0.02	0.07	-0.01	0.69	-0.01
FEAR30	0.07	-0.01	0.05	0.09	-0.04	0.12	0.12	-0.02	-0.03	0.05	0.06	0.03	0.63	-0.04
FEAR31	-0.01	0.11	-0.01	-0.02	-0.12	0.02	0.05	0.00	0.01	0.02	0.76	0.01	0.11	-0.04
SEPR32	-0.04	0.11	0.02	-0.06	-0.02	0.79	-0.06	-0.07	0.08	0.09	-0.02	-0.03	0.06	0.01
SEPR33	-0.05	-0.01	0.03	0.01	-0.06	0.68	-0.01	0.01	0.03	0.04	-0.02	0.03	0.08	0.06
SEPR34	-0.03	-0.09	-0.03	-0.02	0.08	0.82	0.07	0.07	-0.03	-0.07	0.03	0.01	0.02	0.03
EXCITE35	-0.15	0.11	0.02	-0.11	-0.01	0.14	-0.09	-0.03	0.63	0.06	-0.01	0.04	0.00	0.11
EXCITE36	0.17	0.01	0.05	0.00	0.00	-0.06	0.01	-0.01	0.71	-0.01	-0.09	-0.04	0.06	0.07
EXCITE37	-0.08	-0.04	-0.04	0.04	0.01	0.04	-0.01	0.04	0.78	0.00	0.04	-0.01	-0.04	0.02
EXCITE38	0.04	-0.04	-0.13	0.05	-0.04	-0.03	0.09	0.06	0.76	0.01	0.02	0.03	-0.01	-0.02
ATT39	0.03	0.09	0.21	-0.11	0.11	0.10	-0.15	-0.38	0.20	-0.04	0.02	0.28	-0.01	-0.02
ATT40	-0.02	0.06	0.41	0.03	0.08	0.16	0.00	-0.19	0.08	-0.09	0.07	0.27	0.01	-0.22
ATT41	0.07	0.05	0.19	0.06	-0.09	0.11	-0.06	-0.18	0.07	0.05	-0.03	0.52	-0.03	0.01
ATT42	-0.03	0.03	0.14	0.00	-0.03	0.14	0.02	-0.01	0.12	0.09	0.05	0.42	-0.02	0.06
PLAY43	0.49	-0.29	-0.01	-0.01	-0.27	-0.08	0.04	-0.05	0.07	-0.07	0.08	0.03	-0.01	0.13
PLAY44	0.88	-0.02	0.03	-0.02	-0.03	-0.01	-0.03	0.02	0.05	0.05	0.03	-0.03	0.02	0.04
PLAY45	0.81	0.00	-0.01	-0.09	0.05	-0.07	-0.04	-0.06	0.01	-0.05	0.04	0.04	0.03	0.09
PLAY46	0.75	-0.03	-0.15	-0.01	0.10	0.04	0.01	0.07	0.04	-0.02	-0.09	-0.06	-0.01	0.03
IMP47	0.26	0.07	-0.09	-0.03	0.04	0.04	-0.01	0.47	0.13	0.01	0.06	0.28	0.05	0.06
IMP48	0.20	0.05	-0.02	0.11	-0.01	0.06	0.01	0.36	0.10	0.06	0.03	0.33	0.05	0.06
IMP49	0.08	0.01	0.07	0.18	0.03	-0.03	-0.06	0.44	0.14	-0.06	0.08	0.17	0.08	-0.04
MISC50	0.13	-0.04	0.07	0.31	0.00	0.30	0.05	0.14	0.08	-0.16	0.13	0.13	-0.17	-0.01
MISC52	-0.25	-0.14	-0.06	0.00	0.14	-0.10	0.05	0.07	0.06	-0.10	0.07	0.47	0.25	0.04
MISC53	-0.20	-0.18	-0.12	0.16	0.02	0.01	-0.02	0.20	0.02	-0.09	0.04	0.42	0.17	0.06
MISC54	-0.06	0.00	0.13	-0.04	0.00	-0.03	0.66	0.01	0.07	0.00	0.02	0.05	0.14	-0.10
MISC55	-0.01	0.02	-0.07	-0.08	0.02	0.03	0.87	-0.04	0.01	0.06	-0.01	-0.01	-0.03	0.00
MISC56	-0.07	-0.08	0.01	0.14	0.04	-0.02	0.73	-0.02	-0.02	-0.09	0.09	-0.06	0.01	0.08
MISC57	-0.02	-0.05	0.06	0.11	-0.06	0.15	0.00	0.27	0.09	0.04	0.00	0.13	0.00	0.27
MISC58	0.05	-0.04	0.01	0.35	0.00	0.26	0.07	0.06	-0.10	0.00	0.01	0.02	-0.11	0.17
MISC59	0.18	0.09	0.06	0.05	-0.07	0.37	0.04	0.19	-0.03	0.03	-0.04	0.20	0.00	0.34
MISC60	0.12	0.01	0.08	0.00	-0.03	0.05	0.02	-0.05	0.14	-0.10	0.01	0.03	0.01	0.62
MISC61	0.20	0.06	0.02	0.01	0.02	0.15	-0.04	-0.07	0.17	0.01	-0.10	-0.05	-0.06	0.63
MISC62	-0.07	-0.10	0.40	-0.04	0.07	-0.08	0.01	0.07	0.04	0.24	0.28	0.04	0.03	0.26
MISC63	-0.03	-0.04	0.37	0.05	0.06	-0.14	0.13	0.08	0.12	0.02	0.10	0.17	0.02	0.21
MISC64	-0.07	-0.14	0.70	0.05	0.07	0.06	0.03	0.05	-0.05	-0.03	0.00	-0.04	0.05	0.03
MISC65	-0.08	-0.11	0.63	-0.02	0.04	0.04	0.03	0.15	-0.06	0.06	0.07	0.06	0.07	0.05
MISC66	-0.06	0.25	0.57	-0.03	-0.03	0.03	0.19	0.11	-0.07	-0.02	-0.03	0.05	0.08	0.00
MISC67	-0.12	0.24	0.52	0.03	-0.04	0.05	0.17	0.02	-0.07	0.04	-0.02	0.07	0.05	0.04
MISC69	0.01	-0.01	0.07	0.09	0.06	0.15	0.23	0.08	0.04	-0.04	0.14	0.16	-0.23	-0.05
MISC70	0.00	-0.01	-0.09	0.01	0.18	0.15	0.13	0.15	-0.02	0.12	-0.01	0.34	-0.05	0.22
MISC71	0.04	-0.06	0.17	0.02	0.07	0.15	0.21	0.00	-0.08	-0.17	0.11	0.26	-0.06	0.11

2.4.6.4.1 14 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
14	PA1	0.41	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
46	PA1	0.40	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
47	PA1	0.37	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
48	PA1	0.70	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
49	PA1	0.63	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
50	PA1	0.57	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
51	PA1	0.52	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
67	PA1	0.58	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
68	PA1	0.10	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
26	PA10	0.43	FEAR26	When examined/treated by a veterinarian
29	PA10	0.69	FEAR29	When having nails trimmed, or feet touched/handled
30	PA10	0.63	FEAR30	When groomed or bathed
21	PA11	0.80	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
22	PA11	0.35	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
23	PA11	0.78	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
24	PA11	0.80	FEAR24	When an unfamiliar person tries to touch or pet the dog
25	PA11	0.35	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
28	PA11	0.49	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
32	PA12	0.47	IMP47	Impulsive; doesn’t seem to think before s/he acts
33	PA12	0.36	IMP48	Becomes frustrated/impatient in a wide range of situations
34	PA12	0.44	IMP49	Is difficult to interrupt or distract when doing things s/he wants to do
41	PA12	0.27	MISC57	Pulls excessively hard when on leash
62	PA12	0.50	TRAIN01	Is hard to recall when off the leash
63	PA12	0.46	TRAIN02	Is slow to obey a ‘sit’ command
64	PA12	0.66	TRAIN04	Has difficulty attending/listening to things you say or do
65	PA12	0.48	TRAIN05	Is slow to respond to corrections or reprimands: thick-skinned
66	PA12	0.32	TRAIN06	Is slow to learn new tricks or tasks
44	PA13	0.62	MISC60	Playful, puppyish, boisterous
45	PA13	0.63	MISC61	Active, energetic, always on the go
27	PA14	0.82	FEAR27	When approached directly by an unfamiliar dog
31	PA14	0.76	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
55	PA2	0.49	PLAY43	Eagerly engages in play with new/unfamiliar people
56	PA2	0.88	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
57	PA2	0.81	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
58	PA2	0.75	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.71	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.74	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.63	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.70	AGG15	When an unfamiliar person tries to touch or pet the dog
9	PA3	0.41	AGG17	When stared at directly by you or another familiar person
3	PA4	0.81	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.86	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.93	AGG13	When his/her food is taken away by you or another familiar person
35	PA4	0.31	MISC50	NA
42	PA4	0.35	MISC58	Urinates against objects/furnishings indoors
38	PA5	0.66	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
39	PA5	0.87	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
40	PA5	0.73	MISC56	Nervous or frightened when ascending or descending some types of stairs
52	PA5	0.23	MISC69	Chases/follows shadows, light spots, etc.
43	PA6	0.37	MISC59	Hyperactive, restless, has trouble settling down
59	PA6	0.79	SEPR32	Restlessness/agitation/pacing when left alone
60	PA6	0.68	SEPR33	Barking or whining when left alone
61	PA6	0.82	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
13	PA7	0.28	ATT39	Displays a strong attachment for you or another familiar person
15	PA7	0.52	ATT41	Tends to nudge or paw you (or others) for attention
16	PA7	0.42	ATT42	Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
36	PA7	0.47	MISC52	Begs persistently for food when people are eating
37	PA7	0.42	MISC53	Steals food
53	PA7	0.34	MISC70	Barks persistently when alarmed or excited
54	PA7	0.26	MISC71	Licks people or objects excessively
8	PA8	0.60	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA8	0.60	AGG18	When barked, growled, or lunged at by another dog
11	PA8	0.71	AGG19	Towards other familiar dogs
12	PA8	0.61	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
17	PA9	0.63	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
18	PA9	0.71	EXCITE36	Excitable when playing with you or other familiar persons
19	PA9	0.78	EXCITE37	Excitable just before being taken out for a walk
20	PA9	0.76	EXCITE38	Excitable just before being taken out for work or training

2.4.7 14 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.8848002.

The overall omega for all items is 0.929246.

Hierarchical omega is 0.5714398.

2.5 15 Factors

2.5.1 Imputation of Missing Items (15 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.5.2 15-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.5.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.6065968^{4} with 2278 DF, p = 0e+00.

2.5.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8584491

2.5.3 15-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.5.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.0550218^{4} with 2278 DF, p = 0e+00.

2.5.3.2 15-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8584491

2.5.4 Between-Item Correlations

2.5.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175949. The maximum correlation in this data set is 0.8888165.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902169. The maximum correlation was 0.8867879.

2.5.5 Estimating Number of Factors

2.5.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 15.

2.5.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Number of Factors	MAP value
1	0.0252
2	0.0213
3	0.0163
4	0.0146
5	0.0138
6	0.0130
7	0.0127
8	0.0121
9	0.0118
10	0.0116
11	0.0113
12	0.0110
13	0.0113
14	0.0115
15	0.0117
16	0.0120
17	0.0122
18	0.0126

2.5.6 Factor Analysis for 15 Factors

2.5.6.1 15 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 1.9648324^{4}
  
• degrees of freedom: 1363
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4705202. Should be > 0.9; need reference)

2.5.6.2 15 Factor Model Communalities

	fanal15.communality
TRAIN01	0.56
TRAIN02	0.42
TRAIN03	0.52
TRAIN04	0.61
TRAIN05	0.34
TRAIN06	0.34
TRAIN07	0.61
TRAIN08	0.63
AGG09	0.76
AGG10	0.71
AGG11	0.82
AGG12	0.89
AGG13	0.97
AGG14	0.50
AGG15	0.78
AGG16	0.76
AGG17	0.72
AGG18	0.72
AGG19	0.72
AGG20	0.57
FEAR21	0.83
FEAR22	0.42
FEAR23	0.79
FEAR24	0.86
FEAR25	0.49
FEAR26	0.44
FEAR27	0.82
FEAR28	0.67
FEAR29	0.58
FEAR30	0.59
FEAR31	0.67
SEPR32	0.70
SEPR33	0.60
SEPR34	0.74
EXCITE35	0.49
EXCITE36	0.63
EXCITE37	0.59
EXCITE38	0.63
ATT40	0.27
ATT42	0.27
PLAY43	0.56
PLAY44	0.80
PLAY45	0.74
PLAY46	0.72
IMP47	0.47
IMP48	0.49
IMP49	0.40
MISC50	0.34
MISC51	0.48
MISC52	0.44
MISC53	0.46
MISC54	0.62
MISC55	0.73
MISC56	0.62
MISC57	0.35
MISC58	0.25
MISC59	0.57
MISC60	0.58
MISC61	0.69
MISC62	0.52
MISC63	0.40
MISC64	0.59
MISC65	0.63
MISC66	0.69
MISC67	0.62
MISC68	0.24
MISC70	0.36
MISC71	0.29

2.5.6.3 How many communalities < 0.40?

There are 12 items with communality < 0.40.

	fanal15.communality	item
TRAIN05	0.34	TRAIN05
TRAIN06	0.34	TRAIN06
ATT40	0.27	ATT40
ATT42	0.27	ATT42
IMP49	0.40	IMP49
MISC50	0.34	MISC50
MISC57	0.35	MISC57
MISC58	0.25	MISC58
MISC63	0.40	MISC63
MISC68	0.24	MISC68
MISC70	0.36	MISC70
MISC71	0.29	MISC71

2.5.6.4 15 Factor Model Loadings

	PA1	PA15	PA2	PA5	PA3	PA6	PA12	PA7	PA9	PA8	PA11	PA13	PA14	PA10	PA4
TRAIN01	0.13	-0.02	-0.11	-0.10	-0.05	-0.07	0.48	-0.08	-0.06	0.10	0.10	-0.06	0.04	0.10	0.36
TRAIN02	-0.05	-0.01	-0.02	-0.02	0.07	0.02	0.64	0.08	0.04	-0.05	-0.04	0.02	-0.01	0.09	-0.10
TRAIN03	-0.07	-0.01	-0.07	-0.08	0.00	0.08	0.69	0.07	0.04	0.08	0.03	-0.08	0.06	0.08	-0.06
TRAIN04	0.25	0.05	0.00	0.07	-0.05	0.03	0.62	-0.01	-0.01	-0.06	-0.02	0.04	-0.05	-0.06	0.09
TRAIN05	0.09	-0.11	0.06	0.18	0.10	-0.02	0.43	-0.02	0.05	0.03	0.07	-0.05	0.02	-0.13	0.09
TRAIN06	0.12	-0.07	-0.03	0.04	-0.02	0.12	0.44	0.14	-0.05	-0.06	-0.10	0.12	-0.17	-0.04	-0.13
TRAIN07	0.59	0.05	-0.12	0.01	-0.10	0.03	0.28	-0.06	-0.01	0.02	-0.08	0.01	-0.02	0.04	0.04
TRAIN08	0.09	0.02	-0.72	0.02	-0.03	0.01	0.07	0.07	0.04	-0.09	0.01	0.05	0.00	0.04	0.05
AGG09	0.07	0.25	0.05	0.10	0.70	-0.04	0.05	0.05	-0.06	0.02	-0.03	0.02	0.05	-0.03	0.04
AGG10	-0.04	-0.04	0.06	0.07	0.79	0.10	-0.01	-0.02	0.00	0.07	0.01	0.00	-0.05	0.05	-0.03
AGG11	-0.15	0.04	-0.11	0.72	-0.07	0.06	0.04	0.01	-0.14	0.16	0.06	0.01	0.11	0.07	0.25
AGG12	0.04	0.02	-0.06	0.92	0.03	0.04	-0.01	0.03	0.06	0.02	-0.02	0.02	-0.07	-0.05	-0.16
AGG13	0.04	0.01	0.00	0.92	0.09	-0.08	-0.01	-0.01	0.05	0.01	0.01	-0.01	0.01	0.10	0.06
AGG14	0.06	0.06	0.00	-0.08	0.62	0.11	-0.07	0.00	0.06	0.09	0.18	-0.02	-0.12	-0.03	0.03
AGG15	-0.03	0.28	-0.06	0.10	0.68	-0.06	0.02	0.04	-0.05	0.11	0.00	-0.12	0.09	0.08	0.04
AGG16	0.05	-0.06	-0.03	-0.03	0.29	-0.05	0.08	0.05	-0.01	0.61	-0.08	0.28	-0.01	-0.05	-0.06
AGG17	0.11	0.10	0.18	0.14	0.29	0.17	-0.09	0.10	0.14	0.07	-0.23	-0.03	-0.26	0.14	0.42
AGG18	0.03	-0.10	0.03	-0.03	0.30	-0.01	0.04	-0.01	-0.04	0.61	-0.02	0.27	0.03	-0.02	0.00
AGG19	0.00	0.02	0.07	0.12	-0.01	0.03	-0.02	0.02	0.10	0.76	-0.06	0.01	0.02	0.05	0.08
AGG20	-0.02	-0.01	0.06	0.30	-0.11	0.06	-0.04	0.00	0.00	0.59	0.16	-0.06	-0.15	0.08	-0.02
FEAR21	-0.02	0.84	-0.01	0.04	0.07	0.01	0.01	0.01	0.01	-0.01	-0.03	0.08	0.02	0.07	0.04
FEAR22	0.16	0.36	-0.04	-0.07	-0.25	0.03	-0.02	0.23	0.05	0.23	0.11	-0.14	-0.11	0.08	-0.13
FEAR23	0.01	0.76	-0.02	0.01	0.16	0.05	0.00	0.05	0.00	-0.02	-0.03	0.15	0.01	-0.05	-0.02
FEAR24	-0.01	0.82	-0.10	0.05	0.12	-0.02	-0.03	-0.03	0.04	-0.04	-0.03	0.15	0.03	0.03	-0.01
FEAR25	0.25	0.37	0.07	0.07	-0.15	0.01	0.03	0.29	0.04	0.07	0.11	0.03	-0.11	-0.04	0.06
FEAR26	-0.01	0.35	0.05	0.06	0.02	0.05	0.02	-0.01	-0.02	0.02	0.03	0.09	0.03	0.41	-0.01
FEAR27	-0.02	0.19	0.00	0.03	-0.04	0.01	-0.02	0.03	-0.01	0.09	0.00	0.80	-0.02	0.04	0.01
FEAR28	0.14	0.51	0.08	0.00	-0.09	0.03	0.02	0.35	0.05	0.02	-0.02	0.00	-0.08	0.16	-0.07
FEAR29	0.01	-0.04	0.00	0.00	0.05	0.03	0.05	-0.01	0.01	-0.04	0.00	0.06	0.04	0.74	0.03
FEAR30	0.07	-0.01	0.08	0.09	-0.03	0.12	0.00	0.10	-0.03	0.04	0.07	0.04	-0.04	0.64	-0.07
FEAR31	0.00	0.14	-0.01	-0.02	-0.12	0.04	0.00	0.06	0.00	0.04	0.05	0.71	-0.06	0.11	-0.02
SEPR32	0.01	0.08	-0.03	-0.03	0.03	0.81	-0.02	-0.06	0.08	0.06	-0.07	0.00	0.00	0.06	-0.08
SEPR33	0.02	-0.09	-0.04	0.06	0.01	0.73	0.08	0.00	0.01	-0.03	-0.01	0.02	0.06	0.08	-0.13
SEPR34	-0.01	-0.04	-0.02	-0.06	0.03	0.79	0.02	0.07	-0.03	-0.04	0.05	0.02	0.02	0.01	0.22
EXCITE35	0.00	0.10	-0.16	-0.10	0.01	0.14	0.02	-0.09	0.63	0.05	-0.01	0.00	0.13	0.01	-0.04
EXCITE36	0.04	-0.02	0.16	0.03	0.02	-0.05	0.00	0.02	0.71	-0.05	-0.07	-0.06	0.08	0.05	-0.01
EXCITE37	-0.03	-0.01	-0.08	0.04	0.00	0.04	0.02	-0.02	0.77	0.03	0.01	0.02	0.02	-0.04	0.01
EXCITE38	-0.10	0.00	0.05	0.04	-0.07	-0.04	0.01	0.06	0.76	0.04	0.08	0.00	-0.03	-0.01	0.04
ATT40	0.33	0.07	-0.09	-0.03	0.07	0.17	-0.10	0.02	0.10	-0.06	0.11	0.06	-0.14	0.04	-0.02
ATT42	0.16	-0.01	-0.06	-0.01	-0.01	0.15	-0.04	0.04	0.16	0.04	0.26	0.12	0.11	0.00	0.00
PLAY43	0.01	-0.33	0.48	0.01	-0.23	-0.05	-0.06	0.03	0.08	-0.09	0.02	0.10	0.12	-0.01	-0.09
PLAY44	0.00	-0.03	0.85	-0.03	-0.03	-0.01	0.02	-0.03	0.05	0.06	-0.05	0.02	0.06	0.03	-0.01
PLAY45	-0.02	-0.01	0.79	-0.09	0.05	-0.05	-0.08	-0.04	0.02	-0.05	0.01	0.05	0.10	0.02	-0.03
PLAY46	-0.16	0.00	0.75	-0.03	0.06	0.00	0.03	0.01	0.04	0.01	-0.03	-0.10	0.03	-0.02	0.11
IMP47	-0.01	0.07	0.32	0.00	0.04	0.04	0.31	-0.04	0.13	-0.02	0.37	0.09	0.02	0.00	0.05
IMP48	0.08	-0.02	0.26	0.19	0.06	0.11	0.23	-0.01	0.11	-0.03	0.40	0.09	-0.01	-0.01	-0.14
IMP49	0.11	0.04	0.12	0.20	0.00	-0.06	0.32	-0.07	0.13	-0.06	0.25	0.09	-0.05	0.04	0.12
MISC50	0.06	0.01	0.11	0.26	-0.04	0.27	0.09	0.06	0.08	-0.10	0.13	0.11	0.03	-0.14	0.17
MISC51	0.09	-0.02	-0.10	-0.05	-0.03	0.20	0.12	-0.02	0.06	0.10	0.28	-0.03	0.05	-0.08	0.42
MISC52	0.01	-0.09	-0.23	-0.04	0.10	-0.08	-0.05	0.03	0.08	-0.07	0.57	0.06	-0.02	0.19	0.01
MISC53	-0.07	-0.13	-0.17	0.13	0.00	0.01	0.09	-0.04	0.03	-0.06	0.55	0.02	0.00	0.13	0.04
MISC54	0.13	0.02	-0.06	-0.05	-0.02	-0.04	0.02	0.65	0.07	0.01	0.06	0.00	-0.10	0.13	0.02
MISC55	-0.07	-0.01	-0.01	-0.06	0.02	0.02	0.01	0.88	0.00	0.05	-0.03	0.00	0.02	-0.01	-0.02
MISC56	-0.02	-0.07	-0.07	0.13	0.03	-0.03	0.04	0.77	-0.05	-0.06	-0.02	0.06	0.08	0.00	0.03
MISC57	0.09	0.00	0.01	0.09	-0.09	0.11	0.21	-0.02	0.09	0.08	0.19	-0.03	0.25	0.00	0.07
MISC58	0.00	0.04	0.07	0.29	-0.04	0.24	0.06	0.06	-0.11	0.09	0.11	-0.07	0.12	-0.11	0.04
MISC59	0.15	0.11	0.22	0.05	-0.07	0.36	0.07	0.00	-0.03	0.05	0.28	-0.06	0.29	-0.03	-0.03
MISC60	0.05	0.01	0.09	0.00	-0.03	0.03	0.00	0.07	0.11	-0.09	0.00	0.01	0.69	0.03	-0.01
MISC61	0.00	0.09	0.20	-0.01	0.01	0.13	-0.04	-0.03	0.14	0.06	-0.03	-0.13	0.65	-0.04	0.00
MISC62	0.44	-0.09	-0.07	-0.04	0.07	-0.07	0.03	-0.01	0.04	0.25	0.05	0.27	0.24	0.02	-0.02
MISC63	0.44	-0.04	-0.02	0.04	0.07	-0.11	-0.02	0.09	0.15	0.01	0.20	0.10	0.17	0.00	0.00
MISC64	0.73	-0.13	-0.08	0.05	0.05	0.04	0.02	0.00	-0.04	-0.03	-0.09	0.00	0.03	0.06	0.09
MISC65	0.68	-0.08	-0.07	-0.04	0.01	0.03	0.08	-0.02	-0.04	0.08	0.07	0.05	0.02	0.06	0.08
MISC66	0.62	0.22	-0.04	0.00	0.01	0.06	0.08	0.15	-0.06	-0.06	0.04	-0.02	-0.05	0.04	-0.08
MISC67	0.57	0.23	-0.09	0.03	-0.01	0.09	0.00	0.12	-0.06	0.04	0.07	-0.05	-0.03	0.01	-0.15
MISC68	0.08	-0.12	0.06	0.21	0.03	0.08	0.01	0.20	0.07	-0.10	-0.07	0.17	0.04	-0.08	0.28
MISC70	0.03	0.00	0.05	0.01	0.18	0.16	-0.01	0.09	0.00	0.12	0.42	-0.01	0.15	-0.08	-0.02
MISC71	0.23	-0.01	0.03	-0.04	0.03	0.14	-0.10	0.19	-0.04	-0.13	0.28	0.10	0.09	-0.07	0.14

2.5.6.4.1 15 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
13	PA1	0.33	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
45	PA1	0.44	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
46	PA1	0.44	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
47	PA1	0.73	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
48	PA1	0.68	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
49	PA1	0.62	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
50	PA1	0.57	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
67	PA1	0.59	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
68	PA1	0.09	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
24	PA10	0.41	FEAR26	When examined/treated by a veterinarian
27	PA10	0.74	FEAR29	When having nails trimmed, or feet touched/handled
28	PA10	0.64	FEAR30	When groomed or bathed
14	PA11	0.26	ATT42	Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
30	PA11	0.37	IMP47	Impulsive; doesn’t seem to think before s/he acts
31	PA11	0.40	IMP48	Becomes frustrated/impatient in a wide range of situations
35	PA11	0.57	MISC52	Begs persistently for food when people are eating
36	PA11	0.55	MISC53	Steals food
52	PA11	0.42	MISC70	Barks persistently when alarmed or excited
53	PA11	0.28	MISC71	Licks people or objects excessively
32	PA12	0.32	IMP49	Is difficult to interrupt or distract when doing things s/he wants to do
61	PA12	0.48	TRAIN01	Is hard to recall when off the leash
62	PA12	0.64	TRAIN02	Is slow to obey a ‘sit’ command
63	PA12	0.69	TRAIN03	Is slow to obey a ‘stay’ command
64	PA12	0.62	TRAIN04	Has difficulty attending/listening to things you say or do
65	PA12	0.43	TRAIN05	Is slow to respond to corrections or reprimands: thick-skinned
66	PA12	0.44	TRAIN06	Is slow to learn new tricks or tasks
25	PA13	0.80	FEAR27	When approached directly by an unfamiliar dog
29	PA13	0.71	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
40	PA14	0.25	MISC57	Pulls excessively hard when on leash
43	PA14	0.69	MISC60	Playful, puppyish, boisterous
44	PA14	0.65	MISC61	Active, energetic, always on the go
19	PA15	0.84	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
20	PA15	0.36	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
21	PA15	0.76	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
22	PA15	0.82	FEAR24	When an unfamiliar person tries to touch or pet the dog
23	PA15	0.37	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
26	PA15	0.51	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
54	PA2	0.48	PLAY43	Eagerly engages in play with new/unfamiliar people
55	PA2	0.85	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
56	PA2	0.79	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
57	PA2	0.75	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.70	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.79	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.62	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.68	AGG15	When an unfamiliar person tries to touch or pet the dog
9	PA4	0.42	AGG17	When stared at directly by you or another familiar person
34	PA4	0.42	MISC51	Escapes or would escape from home, yard or kennel given the chance
51	PA4	0.28	MISC68	Chases own tail/hind end
3	PA5	0.72	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA5	0.92	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA5	0.92	AGG13	When his/her food is taken away by you or another familiar person
41	PA5	0.29	MISC58	Urinates against objects/furnishings indoors
33	PA6	0.27	MISC50	NA
42	PA6	0.36	MISC59	Hyperactive, restless, has trouble settling down
58	PA6	0.81	SEPR32	Restlessness/agitation/pacing when left alone
59	PA6	0.73	SEPR33	Barking or whining when left alone
60	PA6	0.79	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
37	PA7	0.65	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38	PA7	0.88	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
39	PA7	0.77	MISC56	Nervous or frightened when ascending or descending some types of stairs
8	PA8	0.61	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA8	0.61	AGG18	When barked, growled, or lunged at by another dog
11	PA8	0.76	AGG19	Towards other familiar dogs
12	PA8	0.59	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
15	PA9	0.63	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
16	PA9	0.71	EXCITE36	Excitable when playing with you or other familiar persons
17	PA9	0.77	EXCITE37	Excitable just before being taken out for a walk
18	PA9	0.76	EXCITE38	Excitable just before being taken out for work or training

2.5.7 15 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.887826.

The overall omega for all items is 0.9325033.

Hierarchical omega is 0.600543.

2.6 16 Factors

2.6.1 Imputation of Missing Items (16 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.6.2 16-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.6.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.2748245^{4} with 2080 DF, p = 0e+00.

2.6.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.854217

2.6.3 16-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.6.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 5.7919248^{4} with 2080 DF, p = 0e+00.

2.6.3.2 16-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.854217

2.6.4 Between-Item Correlations

2.6.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175873. The maximum correlation in this data set is 0.8916518.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902439. The maximum correlation was 0.8921351.

2.6.5 Estimating Number of Factors

2.6.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 15.

2.6.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Number of Factors	MAP value
1	0.0262
2	0.0224
3	0.0171
4	0.0153
5	0.0146
6	0.0136
7	0.0131
8	0.0128
9	0.0124
10	0.0124
11	0.0120
12	0.0115
13	0.0116
14	0.0119
15	0.0120
16	0.0125
17	0.0128
18	0.0133

2.6.6 Factor Analysis for 16 Factors

2.6.6.1 16 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 1.7661908^{4}
  
• degrees of freedom: 1160
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4646763. Should be > 0.9; need reference)

2.6.6.2 16 Factor Model Communalities

	fanal16.communality
TRAIN01	0.56
TRAIN02	0.45
TRAIN03	0.54
TRAIN04	0.61
TRAIN05	0.35
TRAIN06	0.34
TRAIN07	0.62
TRAIN08	0.63
AGG09	0.76
AGG10	0.72
AGG11	0.82
AGG12	0.88
AGG13	0.96
AGG14	0.52
AGG15	0.78
AGG16	0.76
AGG17	0.76
AGG18	0.73
AGG19	0.72
AGG20	0.58
FEAR21	0.83
FEAR22	0.48
FEAR23	0.80
FEAR24	0.86
FEAR25	0.52
FEAR26	0.44
FEAR27	0.83
FEAR28	0.66
FEAR29	0.59
FEAR30	0.59
FEAR31	0.69
SEPR32	0.69
SEPR33	0.63
SEPR34	0.74
EXCITE35	0.50
EXCITE36	0.63
EXCITE37	0.60
EXCITE38	0.63
ATT40	0.30
ATT42	0.27
PLAY43	0.58
PLAY44	0.80
PLAY45	0.77
PLAY46	0.76
IMP47	0.53
IMP48	0.58
MISC51	0.44
MISC52	0.60
MISC53	0.49
MISC54	0.63
MISC55	0.73
MISC56	0.64
MISC57	0.35
MISC58	0.28
MISC59	0.61
MISC60	0.57
MISC61	0.71
MISC62	0.47
MISC64	0.62
MISC65	0.64
MISC66	0.69
MISC67	0.62
MISC69	0.25
MISC70	0.34
MISC71	0.26

2.6.6.3 How many communalities < 0.40?

There are 9 items with communality < 0.40.

	fanal16.communality	item
TRAIN05	0.35	TRAIN05
TRAIN06	0.34	TRAIN06
ATT40	0.30	ATT40
ATT42	0.27	ATT42
MISC57	0.35	MISC57
MISC58	0.28	MISC58
MISC69	0.25	MISC69
MISC70	0.34	MISC70
MISC71	0.26	MISC71

2.6.6.4 16 Factor Model Loadings

	PA12	PA1	PA2	PA5	PA3	PA8	PA11	PA9	PA6	PA15	PA14	PA16	PA10	PA13	PA7	PA4
TRAIN01	-0.03	0.15	-0.08	-0.06	-0.06	-0.05	-0.09	-0.06	0.07	0.47	-0.03	0.03	0.08	0.04	0.11	0.36
TRAIN02	-0.01	-0.01	0.04	0.01	0.10	0.04	0.06	0.04	-0.07	0.66	0.05	-0.04	0.07	-0.02	0.02	-0.12
TRAIN03	0.00	-0.04	-0.03	-0.05	0.02	0.09	0.05	0.04	0.07	0.69	-0.06	0.01	0.06	0.05	0.05	-0.06
TRAIN04	0.06	0.26	-0.02	0.07	-0.06	0.01	-0.02	0.00	-0.06	0.56	0.02	0.18	-0.05	-0.07	-0.06	0.10
TRAIN05	-0.09	0.08	0.04	0.18	0.07	-0.02	-0.02	0.05	0.04	0.38	-0.07	0.19	-0.13	0.00	0.00	0.12
TRAIN06	-0.07	0.11	-0.08	0.01	-0.03	0.10	0.13	-0.04	-0.06	0.38	0.10	0.13	-0.01	-0.18	-0.15	-0.09
TRAIN07	0.06	0.62	-0.10	0.01	-0.10	0.01	-0.08	0.00	0.02	0.26	0.01	0.00	0.02	-0.02	-0.02	0.02
TRAIN08	0.00	0.10	-0.68	0.04	-0.03	0.01	0.08	0.04	-0.10	0.08	0.06	-0.11	0.03	0.02	0.08	0.05
AGG09	0.24	0.04	-0.01	0.07	0.68	-0.06	0.07	-0.06	0.04	0.01	0.00	0.11	0.02	0.05	-0.12	0.08
AGG10	-0.04	-0.01	0.09	0.08	0.80	0.11	-0.03	-0.01	0.06	0.01	0.01	-0.03	0.03	-0.05	0.04	-0.04
AGG11	0.04	-0.12	-0.08	0.74	-0.08	0.06	0.00	-0.13	0.14	0.05	0.02	-0.02	0.07	0.11	0.08	0.23
AGG12	0.02	0.04	-0.05	0.91	0.04	0.04	0.03	0.06	0.01	-0.01	0.03	0.02	-0.06	-0.07	-0.03	-0.16
AGG13	0.01	0.05	0.01	0.92	0.08	-0.07	-0.01	0.05	0.01	-0.01	0.00	0.03	0.08	0.00	0.02	0.04
AGG14	0.08	0.07	0.04	-0.07	0.63	0.12	0.00	0.05	0.11	-0.05	-0.02	0.01	-0.08	-0.11	0.20	0.03
AGG15	0.28	-0.02	-0.04	0.12	0.69	-0.06	0.03	-0.05	0.10	0.03	-0.09	-0.04	0.08	0.09	0.02	0.04
AGG16	-0.08	0.05	-0.06	-0.03	0.29	-0.06	0.06	0.00	0.59	0.05	0.30	0.02	-0.05	0.00	-0.11	-0.02
AGG17	0.08	0.14	0.20	0.17	0.26	0.17	0.11	0.16	0.03	-0.10	0.00	-0.14	0.15	-0.24	-0.16	0.46
AGG18	-0.12	0.01	-0.03	-0.05	0.29	-0.03	0.00	-0.04	0.60	0.01	0.27	0.09	0.01	0.03	-0.09	0.04
AGG19	0.02	0.00	0.06	0.12	0.01	0.02	0.00	0.09	0.77	0.02	0.00	-0.06	0.07	0.03	-0.04	0.04
AGG20	-0.01	-0.03	0.02	0.29	-0.11	0.04	-0.01	-0.01	0.60	-0.06	-0.08	0.11	0.10	-0.14	0.09	-0.03
FEAR21	0.82	-0.02	-0.03	0.04	0.07	0.00	0.01	0.01	-0.02	-0.01	0.09	0.02	0.08	0.02	-0.05	0.06
FEAR22	0.39	0.18	0.05	-0.05	-0.22	0.06	0.21	0.03	0.24	0.05	-0.10	-0.14	0.02	-0.11	0.21	-0.18
FEAR23	0.76	-0.01	-0.03	0.01	0.16	0.05	0.04	0.00	-0.02	0.00	0.15	0.02	-0.04	0.01	-0.06	-0.02
FEAR24	0.81	-0.01	-0.10	0.06	0.13	-0.02	-0.04	0.04	-0.04	-0.03	0.16	0.00	0.04	0.03	-0.02	-0.01
FEAR25	0.41	0.24	0.12	0.07	-0.15	0.04	0.26	0.02	0.10	0.06	0.03	0.01	-0.07	-0.12	0.14	0.02
FEAR26	0.34	0.00	0.04	0.06	0.03	0.04	-0.02	-0.02	0.03	0.02	0.09	0.01	0.42	0.04	0.05	-0.03
FEAR27	0.17	0.00	0.04	0.04	-0.04	0.02	0.02	-0.01	0.07	-0.01	0.82	-0.01	0.01	-0.02	0.04	0.01
FEAR28	0.49	0.13	0.07	0.01	-0.09	0.04	0.35	0.05	0.00	0.02	0.03	0.01	0.16	-0.07	-0.04	-0.05
FEAR29	-0.05	-0.01	-0.05	-0.03	0.02	0.01	0.00	0.01	0.00	0.04	0.03	0.01	0.76	0.03	0.02	0.04
FEAR30	-0.01	0.04	0.04	0.06	-0.05	0.10	0.10	-0.03	0.07	0.00	0.02	0.04	0.65	-0.05	0.07	-0.05
FEAR31	0.11	0.03	0.01	0.00	-0.11	0.04	0.06	0.00	0.01	0.00	0.74	0.01	0.09	-0.05	0.06	-0.02
SEPR32	0.07	0.00	-0.05	-0.04	0.03	0.79	-0.06	0.08	0.04	-0.03	0.00	0.04	0.07	0.00	-0.10	-0.07
SEPR33	-0.08	0.03	-0.01	0.08	0.03	0.76	-0.01	0.01	-0.04	0.09	0.04	-0.02	0.03	0.04	0.01	-0.14
SEPR34	-0.03	-0.01	0.00	-0.04	0.02	0.80	0.06	-0.03	-0.04	0.03	0.02	0.02	0.00	0.02	0.05	0.21
EXCITE35	0.11	0.01	-0.13	-0.10	0.02	0.14	-0.10	0.62	0.04	0.04	0.01	-0.03	-0.01	0.13	0.04	-0.05
EXCITE36	-0.02	0.04	0.14	0.02	0.02	-0.06	0.01	0.71	-0.03	-0.01	-0.08	0.04	0.07	0.09	-0.07	-0.03
EXCITE37	-0.03	-0.03	-0.08	0.05	-0.01	0.03	-0.01	0.77	0.01	0.01	0.04	0.03	-0.04	0.03	0.01	0.03
EXCITE38	0.00	-0.11	0.06	0.04	-0.08	-0.03	0.06	0.75	0.04	0.02	0.01	0.04	-0.02	-0.03	0.07	0.05
ATT40	0.05	0.28	-0.19	-0.08	0.05	0.12	0.04	0.11	-0.04	-0.17	0.02	0.23	0.09	-0.13	-0.02	0.02
ATT42	0.02	0.12	-0.10	-0.05	-0.03	0.13	0.04	0.15	0.09	-0.07	0.06	0.23	0.02	0.10	0.16	-0.01
PLAY43	-0.30	0.02	0.53	0.02	-0.23	-0.03	0.02	0.07	-0.08	-0.02	0.12	-0.01	-0.05	0.10	0.06	-0.11
PLAY44	-0.03	0.00	0.81	-0.03	-0.03	-0.02	-0.03	0.05	0.07	0.01	0.02	0.09	0.05	0.06	-0.11	0.00
PLAY45	-0.01	0.00	0.82	-0.07	0.07	-0.05	-0.05	0.01	-0.06	-0.06	0.07	0.02	0.01	0.10	0.01	-0.04
PLAY46	0.01	-0.12	0.81	0.01	0.07	0.03	0.00	0.02	-0.02	0.06	-0.07	-0.04	-0.06	0.02	0.01	0.11
IMP47	0.06	-0.07	0.17	-0.04	0.00	-0.02	-0.01	0.14	0.00	0.17	0.03	0.56	0.06	0.01	0.07	0.11
IMP48	-0.03	0.02	0.11	0.14	0.04	0.05	0.01	0.11	-0.01	0.08	0.02	0.61	0.05	-0.03	0.07	-0.12
MISC51	-0.02	0.06	-0.13	-0.06	-0.05	0.19	-0.02	0.04	0.11	0.10	-0.07	0.20	-0.05	0.06	0.18	0.38
MISC52	-0.06	0.05	-0.08	0.01	0.15	-0.07	0.00	0.06	-0.09	0.00	0.11	0.02	0.09	-0.02	0.72	-0.03
MISC53	-0.10	-0.06	-0.09	0.15	0.00	0.03	-0.05	0.01	-0.06	0.10	0.04	0.16	0.05	0.00	0.55	0.05
MISC54	0.00	0.14	-0.06	-0.05	-0.02	-0.04	0.66	0.07	0.00	0.01	0.01	0.01	0.14	-0.09	0.06	0.03
MISC55	0.01	-0.07	0.00	-0.07	0.02	0.03	0.87	0.00	0.07	0.02	-0.01	-0.04	-0.02	0.01	0.00	-0.04
MISC56	-0.09	-0.02	-0.09	0.14	0.02	-0.04	0.78	-0.04	-0.09	0.02	0.07	0.05	0.02	0.08	-0.05	0.05
MISC57	0.00	0.09	0.03	0.12	-0.09	0.13	-0.01	0.08	0.06	0.20	0.01	0.09	-0.05	0.25	0.16	0.10
MISC58	0.01	0.05	0.11	0.34	-0.02	0.24	0.06	-0.10	0.03	0.05	0.00	0.03	-0.15	0.14	0.09	0.08
MISC59	0.09	0.11	0.09	0.02	-0.10	0.30	0.03	-0.02	0.06	-0.04	-0.09	0.42	0.03	0.31	0.03	0.02
MISC60	0.00	0.06	0.10	-0.01	-0.03	0.01	0.07	0.12	-0.09	0.01	0.01	0.04	0.03	0.67	0.01	-0.03
MISC61	0.07	0.02	0.19	0.00	0.02	0.11	-0.02	0.15	0.05	-0.03	-0.11	-0.01	-0.05	0.67	-0.04	-0.01
MISC62	-0.08	0.39	-0.07	-0.04	0.05	-0.05	0.00	0.04	0.23	0.04	0.28	0.08	0.01	0.21	0.01	0.01
MISC64	-0.14	0.78	-0.03	0.06	0.06	0.03	-0.01	-0.02	-0.05	0.01	0.03	-0.07	0.02	0.04	-0.01	0.08
MISC65	-0.09	0.71	-0.05	-0.03	0.01	0.02	-0.02	-0.04	0.08	0.06	0.06	0.04	0.03	0.04	0.09	0.07
MISC66	0.21	0.61	-0.06	-0.01	0.01	0.04	0.14	-0.06	-0.06	0.05	-0.03	0.11	0.06	-0.04	0.00	-0.09
MISC67	0.20	0.58	-0.10	0.04	0.02	0.06	0.12	-0.05	0.02	-0.02	-0.02	0.06	0.02	0.01	0.03	-0.16
MISC69	0.06	0.09	-0.03	0.02	-0.04	0.09	0.23	0.06	0.03	-0.05	0.11	0.13	-0.20	0.00	0.07	0.25
MISC70	0.01	-0.01	0.01	-0.01	0.17	0.13	0.10	-0.02	0.16	-0.03	-0.04	0.27	-0.06	0.17	0.26	-0.02
MISC71	0.02	0.20	0.02	-0.07	0.01	0.12	0.18	-0.05	-0.08	-0.10	0.04	0.18	-0.05	0.09	0.20	0.10

2.6.6.4.1 16 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
13	PA1	0.28	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
43	PA1	0.39	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
44	PA1	0.78	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
45	PA1	0.71	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
46	PA1	0.61	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
47	PA1	0.58	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
64	PA1	0.62	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
65	PA1	0.10	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
24	PA10	0.42	FEAR26	When examined/treated by a veterinarian
27	PA10	0.76	FEAR29	When having nails trimmed, or feet touched/handled
28	PA10	0.65	FEAR30	When groomed or bathed
35	PA11	0.66	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
36	PA11	0.87	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
37	PA11	0.78	MISC56	Nervous or frightened when ascending or descending some types of stairs
19	PA12	0.82	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
20	PA12	0.39	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
21	PA12	0.76	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
22	PA12	0.81	FEAR24	When an unfamiliar person tries to touch or pet the dog
23	PA12	0.41	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
26	PA12	0.49	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
38	PA13	0.25	MISC57	Pulls excessively hard when on leash
41	PA13	0.67	MISC60	Playful, puppyish, boisterous
42	PA13	0.67	MISC61	Active, energetic, always on the go
25	PA14	0.82	FEAR27	When approached directly by an unfamiliar dog
29	PA14	0.74	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
58	PA15	0.47	TRAIN01	Is hard to recall when off the leash
59	PA15	0.66	TRAIN02	Is slow to obey a ‘sit’ command
60	PA15	0.69	TRAIN03	Is slow to obey a ‘stay’ command
61	PA15	0.56	TRAIN04	Has difficulty attending/listening to things you say or do
62	PA15	0.38	TRAIN05	Is slow to respond to corrections or reprimands: thick-skinned
63	PA15	0.38	TRAIN06	Is slow to learn new tricks or tasks
14	PA16	0.23	ATT42	Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
30	PA16	0.56	IMP47	Impulsive; doesn’t seem to think before s/he acts
31	PA16	0.61	IMP48	Becomes frustrated/impatient in a wide range of situations
40	PA16	0.42	MISC59	Hyperactive, restless, has trouble settling down
49	PA16	0.27	MISC70	Barks persistently when alarmed or excited
51	PA2	0.53	PLAY43	Eagerly engages in play with new/unfamiliar people
52	PA2	0.81	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
53	PA2	0.82	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
54	PA2	0.81	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.68	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.80	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.63	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.69	AGG15	When an unfamiliar person tries to touch or pet the dog
9	PA4	0.46	AGG17	When stared at directly by you or another familiar person
32	PA4	0.38	MISC51	Escapes or would escape from home, yard or kennel given the chance
48	PA4	0.25	MISC69	Chases/follows shadows, light spots, etc.
3	PA5	0.74	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA5	0.91	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA5	0.92	AGG13	When his/her food is taken away by you or another familiar person
39	PA5	0.34	MISC58	Urinates against objects/furnishings indoors
8	PA6	0.59	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA6	0.60	AGG18	When barked, growled, or lunged at by another dog
11	PA6	0.77	AGG19	Towards other familiar dogs
12	PA6	0.60	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
33	PA7	0.72	MISC52	Begs persistently for food when people are eating
34	PA7	0.55	MISC53	Steals food
50	PA7	0.20	MISC71	Licks people or objects excessively
55	PA8	0.79	SEPR32	Restlessness/agitation/pacing when left alone
56	PA8	0.76	SEPR33	Barking or whining when left alone
57	PA8	0.80	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
15	PA9	0.62	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
16	PA9	0.71	EXCITE36	Excitable when playing with you or other familiar persons
17	PA9	0.77	EXCITE37	Excitable just before being taken out for a walk
18	PA9	0.75	EXCITE38	Excitable just before being taken out for work or training

2.6.7 16 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.8814955.

The overall omega for all items is 0.930894.

Hierarchical omega is 0.6054187.

2.7 17 Factors

2.7.1 Imputation of Missing Items (17 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.7.2 17-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.7.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.6272065^{4} with 2278 DF, p = 0e+00.

2.7.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8547232

2.7.3 17-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.7.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.0608085^{4} with 2278 DF, p = 0e+00.

2.7.3.2 17-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8547232

2.7.4 Between-Item Correlations

2.7.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.717562. The maximum correlation in this data set is 0.8902964.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902379. The maximum correlation was 0.8890639.

2.7.5 Estimating Number of Factors

2.7.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 15.

2.7.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Number of Factors	MAP value
1	0.0250
2	0.0213
3	0.0163
4	0.0147
5	0.0139
6	0.0130
7	0.0125
8	0.0122
9	0.0120
10	0.0118
11	0.0115
12	0.0110
13	0.0112
14	0.0116
15	0.0117
16	0.0122
17	0.0123
18	0.0126

2.7.6 Factor Analysis for 17 Factors

2.7.6.1 17 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 1.8817288^{4}
  
• degrees of freedom: 1258
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4489462. Should be > 0.9; need reference)

2.7.6.2 17 Factor Model Communalities

	fanal17.communality
TRAIN01	0.55
TRAIN02	0.43
TRAIN03	0.54
TRAIN04	0.63
TRAIN05	0.34
TRAIN06	0.36
TRAIN07	0.61
TRAIN08	0.63
AGG09	0.79
AGG10	0.73
AGG11	0.86
AGG12	0.90
AGG13	0.95
AGG14	0.51
AGG15	0.80
AGG16	0.76
AGG17	0.77
AGG18	0.73
AGG19	0.72
AGG20	0.60
FEAR21	0.83
FEAR22	0.44
FEAR23	0.80
FEAR24	0.87
FEAR25	0.50
FEAR26	0.44
FEAR27	0.84
FEAR28	0.67
FEAR29	0.61
FEAR30	0.59
FEAR31	0.69
SEPR32	0.67
SEPR33	0.65
SEPR34	0.73
EXCITE35	0.50
EXCITE36	0.62
EXCITE37	0.59
EXCITE38	0.64
ATT39	0.64
ATT40	0.49
ATT42	0.29
PLAY43	0.58
PLAY44	0.81
PLAY45	0.78
PLAY46	0.77
IMP47	0.49
IMP48	0.53
MISC50	0.40
MISC51	0.46
MISC52	0.65
MISC53	0.50
MISC54	0.62
MISC55	0.74
MISC56	0.61
MISC57	0.36
MISC58	0.28
MISC59	0.59
MISC60	0.57
MISC61	0.70
MISC62	0.53
MISC63	0.43
MISC64	0.61
MISC65	0.63
MISC66	0.69
MISC67	0.61
MISC69	0.25
MISC70	0.37
MISC71	0.28

2.7.6.3 How many communalities < 0.40?

There are 9 items with communality < 0.40.

	fanal17.communality	item
TRAIN05	0.34	TRAIN05
TRAIN06	0.36	TRAIN06
ATT42	0.29	ATT42
MISC50	0.40	MISC50
MISC57	0.36	MISC57
MISC58	0.28	MISC58
MISC69	0.25	MISC69
MISC70	0.37	MISC70
MISC71	0.28	MISC71

2.7.6.4 17 Factor Model Loadings

	PA12	PA2	PA1	PA4	PA3	PA5	PA8	PA7	PA9	PA6	PA15	PA17	PA10	PA13	PA11	PA16	PA14
TRAIN01	-0.02	-0.08	0.18	-0.09	-0.04	-0.10	-0.05	-0.04	0.45	0.08	-0.04	0.00	0.09	0.06	0.14	-0.13	0.32
TRAIN02	0.00	0.03	0.00	0.01	0.08	0.08	0.05	0.05	0.64	-0.06	0.04	-0.08	0.06	-0.01	0.04	-0.01	-0.11
TRAIN03	0.00	-0.02	-0.04	-0.06	-0.01	0.07	0.08	0.04	0.69	0.08	-0.07	-0.01	0.04	0.04	0.07	0.03	-0.05
TRAIN04	0.07	-0.02	0.25	0.05	-0.04	-0.03	0.01	0.02	0.59	-0.06	0.03	0.15	-0.03	-0.06	-0.04	-0.11	0.08
TRAIN05	-0.09	0.05	0.10	0.16	0.09	-0.03	-0.03	0.07	0.40	0.05	-0.07	0.14	-0.11	0.01	0.03	-0.06	0.08
TRAIN06	-0.09	-0.06	0.08	0.04	-0.04	0.14	0.07	-0.05	0.44	-0.06	0.10	0.10	-0.01	-0.18	-0.14	0.09	-0.07
TRAIN07	0.07	-0.10	0.59	0.01	-0.11	-0.07	0.03	-0.01	0.27	0.02	0.01	-0.01	0.02	-0.03	-0.01	0.01	0.02
TRAIN08	0.01	-0.69	0.09	0.03	-0.03	0.07	0.02	0.04	0.08	-0.10	0.06	-0.11	0.02	0.02	0.08	0.01	0.05
AGG09	0.22	0.01	0.01	0.10	0.67	0.07	-0.10	-0.07	0.06	0.03	-0.01	0.13	0.03	0.05	-0.12	0.14	0.11
AGG10	-0.04	0.08	-0.02	0.08	0.80	-0.03	0.13	-0.01	-0.01	0.07	0.01	-0.04	0.03	-0.05	0.04	0.01	-0.04
AGG11	0.04	-0.06	-0.13	0.74	-0.10	0.01	0.03	-0.14	0.07	0.15	0.00	-0.01	0.07	0.12	0.10	0.05	0.27
AGG12	0.02	-0.06	0.04	0.92	0.05	0.03	0.04	0.07	-0.02	0.01	0.04	0.03	-0.06	-0.07	-0.04	-0.03	-0.15
AGG13	0.01	0.01	0.06	0.89	0.10	-0.01	-0.07	0.06	-0.02	0.03	-0.01	0.00	0.10	0.00	0.04	-0.05	0.03
AGG14	0.08	0.02	0.06	-0.07	0.60	0.01	0.12	0.05	-0.07	0.11	-0.01	0.05	-0.08	-0.12	0.17	0.03	0.05
AGG15	0.29	-0.05	0.00	0.10	0.70	0.02	-0.04	-0.04	0.01	0.10	-0.09	-0.06	0.07	0.09	0.03	-0.07	0.03
AGG16	-0.08	-0.04	0.04	-0.02	0.27	0.07	-0.07	-0.02	0.09	0.61	0.28	-0.01	-0.06	-0.01	-0.09	0.09	-0.01
AGG17	0.08	0.19	0.14	0.15	0.28	0.10	0.16	0.16	-0.09	0.04	0.01	-0.14	0.15	-0.25	-0.14	-0.04	0.47
AGG18	-0.12	0.00	0.01	-0.04	0.28	0.00	-0.04	-0.05	0.04	0.61	0.26	0.06	0.00	0.03	-0.07	0.08	0.04
AGG19	0.03	0.05	0.02	0.10	0.00	0.01	0.03	0.10	-0.02	0.77	0.00	-0.05	0.06	0.03	-0.05	-0.05	0.04
AGG20	0.02	0.04	-0.03	0.27	-0.12	-0.01	0.05	-0.01	-0.04	0.63	-0.09	0.09	0.09	-0.14	0.10	-0.01	-0.05
FEAR21	0.82	-0.01	-0.03	0.04	0.06	0.01	-0.01	0.00	0.01	-0.01	0.09	0.01	0.07	0.01	-0.04	0.06	0.07
FEAR22	0.38	0.00	0.19	-0.07	-0.22	0.23	0.07	0.04	-0.02	0.22	-0.09	-0.07	0.02	-0.11	0.14	-0.04	-0.16
FEAR23	0.75	-0.04	0.01	0.00	0.18	0.04	0.05	0.01	-0.02	-0.02	0.16	0.03	-0.04	0.02	-0.06	-0.01	-0.03
FEAR24	0.81	-0.08	-0.02	0.06	0.11	-0.03	-0.03	0.02	-0.01	-0.03	0.15	-0.02	0.03	0.02	-0.01	0.09	0.00
FEAR25	0.40	0.09	0.25	0.06	-0.15	0.28	0.02	0.03	0.03	0.09	0.03	0.06	-0.05	-0.11	0.11	-0.02	0.02
FEAR26	0.35	0.06	-0.02	0.06	0.01	-0.02	0.05	-0.03	0.03	0.04	0.08	-0.04	0.40	0.03	0.07	0.06	-0.03
FEAR27	0.17	0.02	0.00	0.04	-0.03	0.01	0.02	0.00	-0.02	0.07	0.84	-0.01	0.02	-0.02	0.04	-0.02	0.02
FEAR28	0.49	0.06	0.14	0.00	-0.07	0.35	0.04	0.06	0.01	0.00	0.04	0.00	0.17	-0.07	-0.05	-0.02	-0.06
FEAR29	-0.05	-0.06	-0.03	-0.03	0.03	-0.01	0.00	0.01	0.03	-0.02	0.03	-0.01	0.79	0.04	0.01	0.01	0.03
FEAR30	-0.01	0.02	0.03	0.06	-0.04	0.10	0.10	-0.02	-0.03	0.05	0.03	0.05	0.66	-0.05	0.04	-0.04	-0.05
FEAR31	0.11	0.00	0.01	-0.01	-0.11	0.05	0.05	0.00	0.00	0.01	0.74	0.00	0.10	-0.05	0.06	0.00	-0.02
SEPR32	0.07	-0.04	-0.01	-0.03	0.02	-0.05	0.77	0.07	-0.01	0.05	0.00	0.02	0.07	0.00	-0.09	0.09	-0.04
SEPR33	-0.08	-0.02	0.05	0.07	0.03	0.00	0.77	0.01	0.08	-0.03	0.04	-0.04	0.04	0.05	0.01	0.01	-0.15
SEPR34	-0.03	-0.02	0.01	-0.06	0.03	0.05	0.78	-0.02	0.01	-0.04	0.02	0.05	0.01	0.03	0.04	-0.04	0.21
EXCITE35	0.12	-0.12	0.01	-0.09	0.00	-0.09	0.15	0.61	0.05	0.05	0.00	-0.05	-0.03	0.12	0.05	0.10	-0.03
EXCITE36	-0.02	0.14	0.03	0.03	0.02	0.01	-0.05	0.70	0.01	-0.03	-0.08	0.00	0.08	0.08	-0.07	0.04	-0.04
EXCITE37	-0.03	-0.07	-0.04	0.05	-0.01	-0.02	0.03	0.76	0.03	0.01	0.04	0.00	-0.04	0.02	0.01	0.04	0.04
EXCITE38	-0.01	0.04	-0.10	0.04	-0.06	0.06	-0.04	0.77	0.00	0.03	0.02	0.05	-0.01	-0.03	0.05	-0.02	0.05
ATT39	0.05	0.08	0.00	-0.05	-0.01	-0.03	0.03	0.08	-0.02	0.03	-0.05	-0.08	-0.03	0.08	0.11	0.75	-0.02
ATT40	0.02	-0.11	0.21	-0.01	-0.02	0.05	0.05	0.04	-0.04	-0.02	-0.02	0.27	0.10	-0.19	-0.02	0.47	0.09
ATT42	0.01	-0.08	0.10	-0.03	-0.04	0.04	0.11	0.14	-0.04	0.09	0.05	0.24	0.02	0.11	0.16	0.12	-0.01
PLAY43	-0.30	0.51	0.04	0.01	-0.22	0.02	-0.02	0.08	-0.06	-0.09	0.12	0.00	-0.04	0.09	0.04	-0.06	-0.12
PLAY44	-0.04	0.84	0.00	-0.02	-0.05	-0.02	-0.03	0.04	0.03	0.07	0.02	0.08	0.05	0.05	-0.11	0.05	0.01
PLAY45	0.00	0.84	0.01	-0.06	0.05	-0.04	-0.05	0.00	-0.05	-0.06	0.07	0.00	0.00	0.08	0.02	0.04	-0.03
PLAY46	0.02	0.82	-0.09	-0.01	0.06	0.01	0.04	0.03	0.04	0.00	-0.07	-0.08	-0.07	0.01	0.04	-0.05	0.10
IMP47	0.05	0.20	-0.07	-0.04	0.05	-0.05	0.00	0.16	0.23	0.01	0.05	0.44	0.09	0.04	0.12	-0.08	0.03
IMP48	-0.02	0.15	0.00	0.14	0.07	-0.02	0.07	0.13	0.16	0.01	0.03	0.47	0.09	0.00	0.13	-0.05	-0.18
MISC50	-0.03	0.01	-0.03	0.24	-0.08	0.07	0.19	0.08	0.06	-0.07	0.06	0.35	-0.05	0.05	-0.08	0.09	0.23
MISC51	-0.03	-0.14	0.07	-0.08	-0.02	-0.04	0.19	0.07	0.09	0.10	-0.05	0.23	-0.03	0.08	0.17	-0.13	0.36
MISC52	-0.03	-0.04	0.05	0.01	0.10	0.03	-0.05	0.03	0.00	-0.07	0.08	-0.03	0.05	-0.04	0.77	0.09	-0.03
MISC53	-0.08	-0.06	-0.06	0.14	-0.02	-0.04	0.03	0.00	0.10	-0.04	0.03	0.13	0.03	-0.01	0.58	0.01	0.03
MISC54	0.01	-0.05	0.12	-0.04	-0.03	0.66	-0.04	0.06	0.03	0.00	0.01	-0.01	0.13	-0.09	0.07	0.03	0.03
MISC55	0.00	-0.02	-0.07	-0.07	0.03	0.88	0.03	0.01	0.00	0.06	-0.01	-0.01	-0.01	0.02	-0.02	-0.04	-0.03
MISC56	-0.08	-0.05	-0.02	0.15	0.02	0.76	-0.04	-0.05	0.06	-0.08	0.06	0.00	0.02	0.08	-0.01	0.04	0.05
MISC57	0.00	0.03	0.13	0.09	-0.07	-0.02	0.14	0.10	0.17	0.06	0.00	0.07	-0.04	0.26	0.18	-0.09	0.06
MISC58	0.03	0.14	0.04	0.33	-0.04	0.07	0.24	-0.12	0.08	0.05	-0.01	0.01	-0.16	0.12	0.12	0.02	0.09
MISC59	0.09	0.12	0.09	0.01	-0.07	0.00	0.31	-0.01	0.02	0.05	-0.08	0.40	0.06	0.30	0.03	-0.03	-0.01
MISC60	0.00	0.11	0.05	0.00	-0.03	0.06	0.03	0.11	0.01	-0.10	-0.01	0.04	0.04	0.66	-0.01	0.06	-0.03
MISC61	0.07	0.20	0.02	0.00	0.01	-0.02	0.13	0.14	-0.05	0.04	-0.12	0.00	-0.05	0.65	-0.06	0.04	0.00
MISC62	-0.10	-0.08	0.44	-0.04	0.08	-0.01	-0.07	0.05	0.01	0.22	0.29	0.07	0.03	0.24	0.02	-0.01	-0.02
MISC63	-0.05	-0.08	0.42	0.02	0.09	0.07	-0.12	0.18	-0.06	-0.01	0.11	0.21	0.05	0.18	0.09	-0.09	-0.03
MISC64	-0.12	-0.03	0.75	0.07	0.04	0.00	0.06	-0.05	0.04	-0.04	0.01	-0.09	0.02	0.03	0.01	0.05	0.09
MISC65	-0.07	-0.05	0.68	-0.03	0.00	-0.01	0.04	-0.06	0.08	0.08	0.06	0.04	0.04	0.02	0.09	0.02	0.07
MISC66	0.22	-0.07	0.58	-0.01	0.01	0.15	0.06	-0.06	0.08	-0.06	-0.02	0.11	0.06	-0.05	-0.01	0.02	-0.10
MISC67	0.21	-0.10	0.53	0.06	-0.01	0.14	0.07	-0.08	0.02	0.02	-0.02	0.08	0.02	-0.02	0.00	0.09	-0.13
MISC69	0.05	-0.03	0.07	0.01	-0.04	0.23	0.08	0.06	-0.02	0.02	0.11	0.18	-0.18	0.00	0.05	0.02	0.26
MISC70	0.00	-0.03	-0.01	-0.02	0.19	0.09	0.14	0.01	-0.06	0.14	-0.02	0.35	-0.03	0.17	0.20	-0.08	-0.03
MISC71	0.01	0.01	0.17	-0.06	0.00	0.18	0.09	-0.05	-0.10	-0.10	0.05	0.27	-0.02	0.09	0.16	0.05	0.12

2.7.6.4.1 17 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
45	PA1	0.44	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
46	PA1	0.42	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
47	PA1	0.75	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
48	PA1	0.68	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
49	PA1	0.58	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
50	PA1	0.53	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
67	PA1	0.59	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
68	PA1	0.09	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
25	PA10	0.40	FEAR26	When examined/treated by a veterinarian
28	PA10	0.79	FEAR29	When having nails trimmed, or feet touched/handled
29	PA10	0.66	FEAR30	When groomed or bathed
35	PA11	0.77	MISC52	Begs persistently for food when people are eating
36	PA11	0.58	MISC53	Steals food
20	PA12	0.82	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
21	PA12	0.38	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
22	PA12	0.75	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
23	PA12	0.81	FEAR24	When an unfamiliar person tries to touch or pet the dog
24	PA12	0.40	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
27	PA12	0.49	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
40	PA13	0.26	MISC57	Pulls excessively hard when on leash
43	PA13	0.66	MISC60	Playful, puppyish, boisterous
44	PA13	0.65	MISC61	Active, energetic, always on the go
9	PA14	0.47	AGG17	When stared at directly by you or another familiar person
34	PA14	0.36	MISC51	Escapes or would escape from home, yard or kennel given the chance
51	PA14	0.26	MISC69	Chases/follows shadows, light spots, etc.
26	PA15	0.84	FEAR27	When approached directly by an unfamiliar dog
30	PA15	0.74	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
13	PA16	0.75	ATT39	Displays a strong attachment for you or another familiar person
14	PA16	0.47	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
15	PA17	0.24	ATT42	Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
31	PA17	0.44	IMP47	Impulsive; doesn’t seem to think before s/he acts
32	PA17	0.47	IMP48	Becomes frustrated/impatient in a wide range of situations
33	PA17	0.35	MISC50	NA
42	PA17	0.40	MISC59	Hyperactive, restless, has trouble settling down
52	PA17	0.35	MISC70	Barks persistently when alarmed or excited
53	PA17	0.27	MISC71	Licks people or objects excessively
54	PA2	0.51	PLAY43	Eagerly engages in play with new/unfamiliar people
55	PA2	0.84	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
56	PA2	0.84	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
57	PA2	0.82	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.67	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.80	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.60	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.70	AGG15	When an unfamiliar person tries to touch or pet the dog
3	PA4	0.74	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.92	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.89	AGG13	When his/her food is taken away by you or another familiar person
41	PA4	0.33	MISC58	Urinates against objects/furnishings indoors
37	PA5	0.66	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38	PA5	0.88	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
39	PA5	0.76	MISC56	Nervous or frightened when ascending or descending some types of stairs
8	PA6	0.61	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA6	0.61	AGG18	When barked, growled, or lunged at by another dog
11	PA6	0.77	AGG19	Towards other familiar dogs
12	PA6	0.63	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
16	PA7	0.61	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
17	PA7	0.70	EXCITE36	Excitable when playing with you or other familiar persons
18	PA7	0.76	EXCITE37	Excitable just before being taken out for a walk
19	PA7	0.77	EXCITE38	Excitable just before being taken out for work or training
58	PA8	0.77	SEPR32	Restlessness/agitation/pacing when left alone
59	PA8	0.77	SEPR33	Barking or whining when left alone
60	PA8	0.78	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
61	PA9	0.45	TRAIN01	Is hard to recall when off the leash
62	PA9	0.64	TRAIN02	Is slow to obey a ‘sit’ command
63	PA9	0.69	TRAIN03	Is slow to obey a ‘stay’ command
64	PA9	0.59	TRAIN04	Has difficulty attending/listening to things you say or do
65	PA9	0.40	TRAIN05	Is slow to respond to corrections or reprimands: thick-skinned
66	PA9	0.44	TRAIN06	Is slow to learn new tricks or tasks

2.7.7 17 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.8852365.

The overall omega for all items is 0.9332413.

Hierarchical omega is 0.6061739.

2.8 18 Factors

2.8.1 Imputation of Missing Items (18 factors)

include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.

Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (2010)

2.8.2 18-Factors: Pre-Imputation Tests for Data Suitability for Factor Analysis

2.8.2.1 Bartlett’s Test of Sphericity

This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.7421286^{4} with 2346 DF, p = 0e+00.

2.8.2.2 Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8539612

2.8.3 18-Factor: Post-Imputation Tests for Data Suitability for Factor Analysis

2.8.3.1 Bartlett’s Test of Sphericity

This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.

The chi-squared for the Bartlett test is 6.1657862^{4} with 2346 DF, p = 0e+00.

2.8.3.2 18-Factor: Kaiser-Meyer-Olkin Criterion (KMO)

From EFAtools::KMO documentation:

The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis

The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.

## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.

[1] 0.8539612

2.8.4 Between-Item Correlations

2.8.4.1 Pre-Imputation

For factor analysis, it is recommended that some of the item correlationsshould be between 0.3 and 0.9. Polyserial correlations were computed using the lavCor function in the lavaan package in R with options for ordered factors and pairwise handling of missing values. Pairwise deletion of missing values means that individuals with some missing data are not dropped; their data is used when available.

The minimum correlation in this data set is -0.7175677. The maximum correlation in this data set is 0.8898946.

#### Post-Imputation

The post imputation polyserial correlation was also computed using the lavcor function, but with no setting for missing values since they were imputed and cor.smooth = TRUE to avoid having a non-positive-definite matrix to work on in future steps.

The minimum correlation was -0.6902114. The maximum correlation was 0.8877677.

2.8.5 Estimating Number of Factors

2.8.5.1 Parallel method

From the EFAtools documentation:

Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.

Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not PCA) - fm = “wls” (weighted least squares because pa gave errors and weighted recommended for ordinal data. - use = “all.obs” (since we have imputed missing values, we can use all data points) - cor = “poly” (use polychoric correlation matrix) - n.iter = 100 (run for 100 iterations)

The suggested number of factors is 15.

2.8.5.2 Minimum Average Partial

MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Number of Factors	MAP value
1	0.0246
2	0.0209
3	0.0161
4	0.0145
5	0.0138
6	0.0129
7	0.0125
8	0.0122
9	0.0122
10	0.0118
11	0.0117
12	0.0113
13	0.0112
14	0.0115
15	0.0117
16	0.0120
17	0.0124
18	0.0124

2.8.6 Factor Analysis for 18 Factors

2.8.6.1 18 Factors Model Fit

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.

• chi-square: 1.9000958^{4}
  
• degrees of freedom: 1257
  
• P-value for chi-square = 0e+00

Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.4352052. Should be > 0.9; need reference)

2.8.6.2 18 Factor Model Communalities

	fanal18.communality
TRAIN01	0.56
TRAIN02	0.43
TRAIN03	0.53
TRAIN04	0.64
TRAIN05	0.34
TRAIN06	0.36
TRAIN07	0.63
TRAIN08	0.63
AGG09	0.80
AGG10	0.73
AGG11	0.86
AGG12	0.89
AGG13	0.97
AGG14	0.52
AGG15	0.79
AGG16	0.76
AGG17	0.80
AGG18	0.73
AGG19	0.72
AGG20	0.60
FEAR21	0.83
FEAR22	0.43
FEAR23	0.80
FEAR24	0.87
FEAR25	0.52
FEAR26	0.44
FEAR27	0.83
FEAR28	0.67
FEAR29	0.64
FEAR30	0.58
FEAR31	0.71
SEPR32	0.67
SEPR33	0.67
SEPR34	0.73
EXCITE35	0.50
EXCITE36	0.62
EXCITE37	0.61
EXCITE38	0.64
ATT39	0.65
ATT40	0.49
ATT42	0.32
PLAY43	0.58
PLAY44	0.81
PLAY45	0.78
PLAY46	0.77
IMP47	0.49
IMP48	0.52
MISC50	0.38
MISC51	0.46
MISC52	0.63
MISC53	0.51
MISC54	0.62
MISC55	0.76
MISC56	0.64
MISC57	0.36
MISC58	0.36
MISC59	0.62
MISC60	0.58
MISC61	0.69
MISC62	0.53
MISC63	0.43
MISC64	0.61
MISC65	0.63
MISC66	0.69
MISC67	0.64
MISC68	0.68
MISC69	0.39
MISC70	0.37
MISC71	0.30

2.8.6.3 How many communalities < 0.40?

There are 9 items with communality < 0.40.

	fanal18.communality	item
TRAIN05	0.34	TRAIN05
TRAIN06	0.36	TRAIN06
ATT42	0.32	ATT42
MISC50	0.38	MISC50
MISC57	0.36	MISC57
MISC58	0.36	MISC58
MISC69	0.39	MISC69
MISC70	0.37	MISC70
MISC71	0.30	MISC71

2.8.6.4 18 Factor Model Loadings

	PA16	PA2	PA1	PA4	PA3	PA6	PA5	PA10	PA11	PA8	PA12	PA18	PA9	PA14	PA7	PA13	PA15	PA17
TRAIN01	-0.03	-0.09	0.16	-0.11	-0.04	-0.06	-0.10	-0.03	0.46	0.07	-0.03	0.03	0.08	0.06	0.15	0.01	-0.13	0.31
TRAIN02	0.01	0.04	0.00	0.02	0.08	0.06	0.09	0.05	0.64	-0.06	0.04	-0.09	0.06	-0.01	0.03	-0.05	-0.01	-0.09
TRAIN03	0.00	-0.02	-0.04	-0.05	-0.02	0.08	0.08	0.05	0.69	0.08	-0.07	-0.01	0.04	0.04	0.06	-0.05	0.03	-0.03
TRAIN04	0.08	-0.02	0.23	0.04	-0.04	0.00	-0.05	0.01	0.60	-0.05	0.02	0.12	-0.02	-0.06	-0.04	0.14	-0.10	0.02
TRAIN05	-0.07	0.04	0.08	0.15	0.10	-0.03	-0.06	0.05	0.41	0.06	-0.09	0.12	-0.09	0.01	0.04	0.12	-0.05	0.01
TRAIN06	-0.09	-0.06	0.07	0.04	-0.04	0.07	0.15	-0.04	0.44	-0.07	0.11	0.11	-0.02	-0.18	-0.15	-0.02	0.08	-0.05
TRAIN07	0.08	-0.10	0.58	0.00	-0.11	0.03	-0.08	-0.03	0.28	0.03	-0.01	-0.04	0.04	-0.03	-0.01	0.12	0.02	-0.02
TRAIN08	0.00	-0.69	0.09	0.03	-0.03	0.02	0.07	0.04	0.07	-0.10	0.06	-0.10	0.02	0.02	0.08	-0.01	0.01	0.06
AGG09	0.21	0.01	0.01	0.09	0.66	-0.10	0.06	-0.07	0.06	0.03	0.00	0.15	0.02	0.05	-0.12	0.01	0.14	0.12
AGG10	-0.03	0.08	-0.01	0.09	0.79	0.13	-0.03	-0.01	-0.01	0.07	0.01	-0.05	0.03	-0.05	0.03	0.00	0.01	-0.02
AGG11	0.03	-0.08	-0.14	0.71	-0.10	0.02	0.00	-0.13	0.07	0.15	0.01	0.02	0.07	0.12	0.11	0.06	0.04	0.29
AGG12	0.02	-0.06	0.05	0.91	0.05	0.05	0.03	0.08	-0.02	0.02	0.04	0.02	-0.05	-0.07	-0.04	-0.02	-0.04	-0.11
AGG13	0.03	0.00	0.05	0.89	0.10	-0.07	-0.03	0.05	-0.01	0.03	-0.02	-0.02	0.11	0.00	0.04	0.10	-0.04	0.01
AGG14	0.10	0.02	0.06	-0.08	0.60	0.12	-0.01	0.03	-0.07	0.12	-0.03	0.02	-0.06	-0.12	0.18	0.08	0.03	0.00
AGG15	0.29	-0.05	0.00	0.11	0.69	-0.03	0.03	-0.03	0.00	0.10	-0.08	-0.05	0.06	0.09	0.03	-0.03	-0.07	0.07
AGG16	-0.08	-0.03	0.04	-0.02	0.27	-0.06	0.07	-0.02	0.09	0.61	0.29	-0.01	-0.06	0.00	-0.09	-0.02	0.09	0.00
AGG17	0.07	0.17	0.13	0.12	0.27	0.14	0.08	0.17	-0.10	0.04	0.02	-0.09	0.14	-0.24	-0.13	0.07	-0.05	0.53
AGG18	-0.12	0.00	0.01	-0.04	0.27	-0.04	0.00	-0.04	0.04	0.62	0.26	0.07	0.00	0.03	-0.07	-0.01	0.07	0.04
AGG19	0.04	0.05	0.02	0.10	0.00	0.03	0.01	0.09	-0.02	0.77	0.00	-0.05	0.07	0.04	-0.05	0.04	-0.05	0.05
AGG20	0.02	0.04	-0.03	0.27	-0.12	0.05	-0.01	-0.02	-0.04	0.64	-0.09	0.08	0.10	-0.14	0.10	0.02	-0.01	-0.06
FEAR21	0.82	-0.01	-0.03	0.04	0.06	-0.01	0.01	0.00	0.02	-0.01	0.09	0.03	0.07	0.02	-0.04	-0.01	0.06	0.08
FEAR22	0.37	0.00	0.21	-0.05	-0.23	0.08	0.25	0.05	-0.02	0.21	-0.08	-0.06	0.02	-0.11	0.13	-0.10	-0.05	-0.10
FEAR23	0.76	-0.04	0.01	0.00	0.17	0.05	0.03	0.00	-0.01	-0.02	0.15	0.02	-0.03	0.02	-0.06	0.04	-0.01	-0.05
FEAR24	0.81	-0.09	-0.02	0.06	0.11	-0.03	-0.04	0.01	-0.01	-0.03	0.15	-0.02	0.03	0.02	-0.02	0.01	0.09	0.00
FEAR25	0.41	0.09	0.25	0.05	-0.15	0.01	0.25	0.02	0.03	0.10	0.02	0.04	-0.04	-0.11	0.11	0.14	-0.01	-0.02
FEAR26	0.35	0.06	-0.01	0.07	0.00	0.05	-0.01	-0.04	0.03	0.04	0.08	-0.04	0.40	0.03	0.06	-0.01	0.06	-0.01
FEAR27	0.17	0.02	0.00	0.02	-0.03	0.01	-0.01	-0.01	-0.02	0.08	0.82	-0.02	0.02	-0.02	0.04	0.07	-0.02	-0.01
FEAR28	0.48	0.06	0.15	0.01	-0.08	0.04	0.36	0.07	0.01	-0.01	0.05	0.03	0.15	-0.07	-0.05	-0.10	-0.03	0.01
FEAR29	-0.04	-0.05	-0.03	-0.03	0.03	0.01	-0.01	-0.01	0.03	-0.01	0.03	-0.02	0.80	0.04	0.02	0.03	0.02	0.01
FEAR30	-0.01	0.03	0.04	0.07	-0.04	0.11	0.11	-0.02	-0.03	0.05	0.05	0.06	0.64	-0.05	0.04	-0.05	-0.04	-0.01
FEAR31	0.10	0.00	0.01	-0.01	-0.10	0.05	0.05	0.02	0.00	0.00	0.77	0.01	0.09	-0.05	0.06	-0.03	-0.01	0.01
SEPR32	0.06	-0.04	0.00	-0.02	0.02	0.77	-0.04	0.08	-0.01	0.04	0.01	0.05	0.05	0.00	-0.10	-0.05	0.09	0.01
SEPR33	-0.07	-0.01	0.05	0.08	0.04	0.78	0.00	-0.01	0.08	-0.03	0.03	-0.06	0.05	0.04	0.01	0.01	0.02	-0.16
SEPR34	-0.03	-0.03	-0.01	-0.08	0.03	0.76	0.03	-0.02	0.01	-0.04	0.02	0.06	0.02	0.03	0.05	0.12	-0.04	0.19
EXCITE35	0.12	-0.12	0.00	-0.09	-0.01	0.15	-0.09	0.60	0.05	0.05	-0.01	-0.07	-0.02	0.12	0.04	0.05	0.10	-0.05
EXCITE36	-0.02	0.15	0.03	0.03	0.02	-0.05	0.01	0.69	0.01	-0.03	-0.08	-0.01	0.08	0.08	-0.07	0.04	0.05	-0.04
EXCITE37	-0.04	-0.07	-0.04	0.05	-0.01	0.03	-0.01	0.78	0.03	0.01	0.05	0.02	-0.05	0.03	0.01	-0.04	0.04	0.07
EXCITE38	-0.01	0.04	-0.10	0.03	-0.06	-0.04	0.05	0.78	0.00	0.03	0.02	0.05	-0.01	-0.03	0.05	0.00	-0.03	0.05
ATT39	0.05	0.08	0.00	-0.05	-0.01	0.03	-0.03	0.07	-0.02	0.03	-0.05	-0.08	-0.01	0.07	0.10	0.01	0.76	-0.03
ATT40	0.00	-0.12	0.20	-0.02	-0.02	0.05	0.04	0.05	-0.04	-0.03	-0.01	0.29	0.09	-0.19	-0.02	0.02	0.46	0.09
ATT42	0.03	-0.08	0.09	-0.05	-0.04	0.11	0.00	0.11	-0.03	0.11	0.02	0.20	0.06	0.10	0.17	0.19	0.13	-0.13
PLAY43	-0.29	0.51	0.04	0.01	-0.22	-0.02	0.02	0.07	-0.06	-0.09	0.11	-0.03	-0.04	0.09	0.04	0.06	-0.06	-0.14
PLAY44	-0.03	0.84	0.00	-0.02	-0.04	-0.03	-0.02	0.04	0.04	0.07	0.01	0.08	0.05	0.05	-0.10	0.01	0.05	0.01
PLAY45	0.00	0.85	0.01	-0.06	0.05	-0.04	-0.03	0.00	-0.05	-0.06	0.07	0.00	-0.01	0.08	0.02	-0.04	0.04	-0.01
PLAY46	0.02	0.82	-0.09	-0.02	0.06	0.04	0.00	0.03	0.04	0.00	-0.08	-0.08	-0.07	0.02	0.04	0.02	-0.05	0.11
IMP47	0.05	0.21	-0.07	-0.05	0.05	-0.01	-0.06	0.16	0.24	0.01	0.05	0.42	0.09	0.03	0.13	0.07	-0.08	-0.03
IMP48	-0.03	0.16	0.00	0.16	0.07	0.07	-0.02	0.13	0.16	0.00	0.05	0.45	0.08	-0.01	0.13	0.03	-0.05	-0.20
MISC50	-0.02	0.01	-0.04	0.20	-0.07	0.17	0.03	0.09	0.07	-0.06	0.04	0.34	-0.04	0.04	-0.05	0.15	0.08	0.16
MISC51	-0.03	-0.15	0.05	-0.11	-0.01	0.17	-0.07	0.08	0.09	0.10	-0.06	0.24	-0.03	0.08	0.19	0.14	-0.13	0.29
MISC52	-0.04	-0.05	0.05	0.01	0.10	-0.05	0.04	0.04	-0.01	-0.08	0.09	-0.03	0.06	-0.04	0.76	-0.04	0.09	-0.02
MISC53	-0.08	-0.06	-0.06	0.14	-0.02	0.03	-0.05	0.00	0.11	-0.05	0.03	0.11	0.04	-0.01	0.59	0.02	0.02	-0.01
MISC54	0.01	-0.05	0.13	-0.04	-0.03	-0.03	0.65	0.07	0.03	0.01	0.02	0.01	0.12	-0.09	0.08	-0.04	0.02	0.06
MISC55	0.03	-0.02	-0.07	-0.09	0.03	0.03	0.85	-0.01	0.00	0.07	-0.03	-0.04	0.01	0.01	-0.01	0.14	-0.04	-0.09
MISC56	-0.09	-0.06	-0.02	0.14	0.02	-0.04	0.77	-0.03	0.05	-0.09	0.08	0.03	0.01	0.08	-0.01	0.00	0.03	0.10
MISC57	0.01	0.03	0.12	0.08	-0.07	0.14	-0.02	0.10	0.18	0.06	-0.01	0.07	-0.03	0.26	0.19	0.03	-0.09	0.03
MISC58	0.00	0.14	0.04	0.33	-0.05	0.24	0.10	-0.09	0.07	0.03	0.03	0.06	-0.21	0.13	0.13	-0.16	0.01	0.22
MISC59	0.07	0.12	0.08	0.02	-0.07	0.31	0.01	0.01	0.01	0.04	-0.06	0.44	0.04	0.29	0.03	-0.05	-0.04	0.02
MISC60	0.01	0.11	0.05	-0.01	-0.03	0.03	0.06	0.10	0.01	-0.09	-0.01	0.03	0.05	0.66	-0.01	0.07	0.06	-0.07
MISC61	0.07	0.20	0.02	-0.01	0.01	0.13	-0.02	0.15	-0.05	0.04	-0.12	0.02	-0.05	0.64	-0.06	0.00	0.04	0.00
MISC62	-0.11	-0.08	0.44	-0.04	0.08	-0.06	-0.01	0.06	0.01	0.22	0.29	0.08	0.02	0.24	0.02	-0.02	-0.02	-0.02
MISC63	-0.05	-0.08	0.42	0.02	0.09	-0.12	0.06	0.18	-0.06	0.00	0.10	0.21	0.05	0.17	0.10	0.01	-0.10	-0.06
MISC64	-0.12	-0.04	0.73	0.05	0.04	0.05	-0.01	-0.06	0.05	-0.04	0.00	-0.09	0.03	0.03	0.01	0.09	0.06	0.08
MISC65	-0.07	-0.06	0.66	-0.04	0.00	0.04	-0.02	-0.06	0.08	0.08	0.06	0.04	0.04	0.02	0.09	0.05	0.02	0.07
MISC66	0.21	-0.07	0.58	0.01	0.02	0.06	0.16	-0.05	0.08	-0.07	-0.01	0.12	0.05	-0.05	-0.01	-0.02	0.01	-0.06
MISC67	0.18	-0.10	0.55	0.08	-0.01	0.08	0.16	-0.05	0.01	0.00	0.01	0.13	0.00	-0.02	0.00	-0.18	0.08	-0.03
MISC68	-0.01	0.01	0.01	0.09	0.00	0.02	0.08	-0.01	0.00	-0.01	0.02	-0.04	0.03	0.02	-0.05	0.79	0.00	-0.04
MISC69	0.10	-0.04	0.03	-0.05	-0.04	0.04	0.15	0.01	-0.02	0.05	0.06	0.11	-0.14	-0.01	0.07	0.49	0.04	0.08
MISC70	0.00	-0.02	-0.01	-0.02	0.19	0.14	0.07	0.02	-0.06	0.14	-0.02	0.34	-0.03	0.16	0.22	0.02	-0.08	-0.07
MISC71	0.01	0.00	0.16	-0.08	0.00	0.08	0.14	-0.06	-0.10	-0.10	0.04	0.26	-0.01	0.08	0.17	0.19	0.05	0.06

2.8.6.4.1 18 Factor Model Largest Loading Per Item

Largest Loading Per Item and Associated Factors, Sorted by Factor

	largest	maximum	itemNames	itemDescriptions
45	PA1	0.44	MISC62	Becomes highly excited and/or distracted when encountering unfamiliar dogs
46	PA1	0.42	MISC63	Becomes highly excited and/or distracted when encountering unfamiliar people
47	PA1	0.73	MISC64	When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects
48	PA1	0.66	MISC65	Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.)
49	PA1	0.58	MISC66	Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work
50	PA1	0.55	MISC67	Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work
68	PA1	0.58	TRAIN07	Unfocused; is easily distracted by interesting sights, sounds or smells
69	PA1	0.09	TRAIN08	Is uninterested in ‘fetching’ or attempting to fetch sticks, toys, balls, or objects
16	PA10	0.60	EXCITE35	Excitable when you first arrive home, or at the dog’s kennel, after a brief absence
17	PA10	0.69	EXCITE36	Excitable when playing with you or other familiar persons
18	PA10	0.78	EXCITE37	Excitable just before being taken out for a walk
19	PA10	0.78	EXCITE38	Excitable just before being taken out for work or training
62	PA11	0.46	TRAIN01	Is hard to recall when off the leash
63	PA11	0.64	TRAIN02	Is slow to obey a ‘sit’ command
64	PA11	0.69	TRAIN03	Is slow to obey a ‘stay’ command
65	PA11	0.60	TRAIN04	Has difficulty attending/listening to things you say or do
66	PA11	0.41	TRAIN05	Is slow to respond to corrections or reprimands: thick-skinned
67	PA11	0.44	TRAIN06	Is slow to learn new tricks or tasks
26	PA12	0.82	FEAR27	When approached directly by an unfamiliar dog
30	PA12	0.77	FEAR31	When barked, growled, or lunged at by an unfamiliar dog
51	PA13	0.79	MISC68	Chases own tail/hind end
52	PA13	0.49	MISC69	Chases/follows shadows, light spots, etc.
40	PA14	0.26	MISC57	Pulls excessively hard when on leash
43	PA14	0.66	MISC60	Playful, puppyish, boisterous
44	PA14	0.64	MISC61	Active, energetic, always on the go
13	PA15	0.76	ATT39	Displays a strong attachment for you or another familiar person
14	PA15	0.46	ATT40	Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler
20	PA16	0.82	FEAR21	When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel
21	PA16	0.37	FEAR22	In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.)
22	PA16	0.76	FEAR23	When an unfamiliar person visits your home or approaches the dog when in his/her home kennel
23	PA16	0.81	FEAR24	When an unfamiliar person tries to touch or pet the dog
24	PA16	0.41	FEAR25	In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc.
27	PA16	0.48	FEAR28	When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.)
9	PA17	0.53	AGG17	When stared at directly by you or another familiar person
34	PA17	0.29	MISC51	Escapes or would escape from home, yard or kennel given the chance
15	PA18	0.20	ATT42	Becomes agitated (whines, jumps up, tries to intervene) when attention is given to another person or animal
31	PA18	0.42	IMP47	Impulsive; doesn’t seem to think before s/he acts
32	PA18	0.45	IMP48	Becomes frustrated/impatient in a wide range of situations
33	PA18	0.34	MISC50	NA
42	PA18	0.44	MISC59	Hyperactive, restless, has trouble settling down
53	PA18	0.34	MISC70	Barks persistently when alarmed or excited
54	PA18	0.26	MISC71	Licks people or objects excessively
55	PA2	0.51	PLAY43	Eagerly engages in play with new/unfamiliar people
56	PA2	0.84	PLAY44	Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person
57	PA2	0.85	PLAY45	Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown
58	PA2	0.82	PLAY46	Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task
1	PA3	0.66	AGG09	Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash
2	PA3	0.79	AGG10	Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel
6	PA3	0.60	AGG14	When strangers walk past when the dog is in his/her home run or kennel
7	PA3	0.69	AGG15	When an unfamiliar person tries to touch or pet the dog
3	PA4	0.71	AGG11	Barks, etc. when toys, bones or other objects are taken away by you or another familiar person
4	PA4	0.91	AGG12	When you or another familiar person approaches the dog directly while s/he is eating
5	PA4	0.89	AGG13	When his/her food is taken away by you or another familiar person
41	PA4	0.33	MISC58	Urinates against objects/furnishings indoors
37	PA5	0.65	MISC54	Reluctant to/nervous about crossing grates or other unfamiliar surfaces
38	PA5	0.85	MISC55	Reluctant to/nervous about crossing shiny or slippery floors
39	PA5	0.77	MISC56	Nervous or frightened when ascending or descending some types of stairs
59	PA6	0.77	SEPR32	Restlessness/agitation/pacing when left alone
60	PA6	0.78	SEPR33	Barking or whining when left alone
61	PA6	0.76	SEPR34	Chewing/scratching at doors, floor, fencing, etc., when left alone
35	PA7	0.76	MISC52	Begs persistently for food when people are eating
36	PA7	0.59	MISC53	Steals food
8	PA8	0.61	AGG16	When approached directly by an unfamiliar dog while being walked/exercised on a leash
10	PA8	0.62	AGG18	When barked, growled, or lunged at by another dog
11	PA8	0.77	AGG19	Towards other familiar dogs
12	PA8	0.64	AGG20	When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog
25	PA9	0.40	FEAR26	When examined/treated by a veterinarian
28	PA9	0.80	FEAR29	When having nails trimmed, or feet touched/handled
29	PA9	0.64	FEAR30	When groomed or bathed

2.8.7 18 Model Reliability Measures

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect.  Try a
## different factor score estimation method.

The overall alpha for all items is 0.8850577.

The overall omega for all items is 0.9334918.

Hierarchical omega is 0.6177792.